The star, who was also known for his Shakespearean roles, had been battling a serious lung condition for a number of years.
Briers, who also starred in shows such as Ever Decreasing Circles and Monarch Of The Glen, recently said years of smoking had been to blame for his emphysema.
Briers died "peacefully" at his London home yesterday, his agent said today.
Briers will be best remembered for his performance as Tom Good, alongside Felicity Kendal, in the 1970s BBC1 sitcom The Good Life about a couple who drop out of the rat race in Surbiton, south west London, to enjoy a life of simply self-sufficiency.
In an interview carried out only a matter of weeks ago, the actor told how his health was failing after being diagnosed with emphysema five years ago, which he attributed to years of smoking, although he gave up 10 years ago.
"I was diagnosed five years ago and didn't think it would go quite as badly as it has. It's a bugger, but there it is. I used to love smoking.
"It's totally my fault. So, I get very breathless, which is a pain in the backside. Trying to get upstairs... oh God, it's ridiculous. Of course, when you're bloody nearly 80 it's depressing, because you've had it anyway."
His agent, Christopher Farrar, of Hamilton Hodell, said: "Richard was a wonderful man, a consummate professional and an absolute joy to work alongside.
"Following his recent discussion of his battle with emphysema, I know he was incredibly touched by the strength of support expressed by friends and the public.
"He has a unique and special place in the hearts of so many. He will be greatly missed. Our thoughts and deepest sympathy go to his family at this sad time."
Briers varied career saw him narrating the 1970s children's cartoon series Roobarb And Custard, as well as adding his voice to the animated version of Watership Down.
He starred as Hector MacDonald in Highland based drama Monarch of the Glen and also appeared on stage in Edinburgh and alongside Scots actor Sylvester McCoy in 1987 in Doctor Who.
However, he will be best remembered for his role as Tom Good, alongside Felicity Kendal, Penelope Keith and Paul Eddington in The Good Life. Eddington passed away in 1995 at the age of 68. Penelope Keith has been trying to open a restaurant in Avoch in the Black Isle.
Although long known for his comedy roles in film and TV, a new strand to his career unfolded when he joined Sir Kenneth Branagh's Renaissance Theatre Company in 1987, and went on to work on a number of classical roles.
Sir Kenneth spoke fondly as he paid tribute to Briers today. saying: "He was a national treasure, a great actor and a wonderful man. He was greatly loved and he will be deeply missed."
They worked together on Henry V, Peter's Friends, Much Ado About Nothing and Mary Shelley's Frankenstein during their lengthy association.
Rada-trained Briers made his West End debut in the late 1950s in Gilt And Gingerbread, and went on to work on a number of British films - Bottoms Up, Murder She Said, The Girl On The Boat and Fathom, alongside Raquel Welch.
He struck gold as an actor with his many sitcoms in the 1970s and 1980s, although none more so than The Good life in which he starred with Penelope Keith, Felicity Kendal and the late Paul Eddington, who died in 1995.
Briers also returned to the stage many times in his career, with numerous roles in the works of Alan Ayckbourn, including Relatively Speaking, Absurd Person Singular and Absent Friends.
His most recent performances have included roles in last year's Cockneys Versus Zombies, plus a small role in a newly released movie version of stage farce Run For Your Wife.
Peter Egan, his co-star in Ever Decreasing Circles, said: "I spent nearly 10 years just laughing. He was just the most magical comedian, a huge talent, has been a part of the nation's lives for over 50 years."
Speaking to Radio Berkshire, Egan went on: "He is a centre-piece of our humorous culture and a magnificently talented man. I'm so deeply sad today that he has left us. He was a great person."
His godson, the actor and director Samuel West - whose mother Prunella Scales appeared alongside Briers in Marriage Lines - said on Twitter: "What a lot of joy he spread."
Briers's former co-star Scales said today: "He was just a wonderful colleague and a dear friend."
She told BBC Radio 5 Live she would always be "so grateful to him" for encouraging her to read for the part of his wife in Marriage Lines. Scales and her husband Timothy West were newly married at the time.
"To have an income like that was absolutely magical, it was very hard work of course, one episode a week," she added.
And former BBC chairman Michael Grade told the radio station: "I think the nation has lost one of its most favourite, favourite, favourite actors of all time - he's sort of up there with Ronnie Barker and Alan Bennett, you know, the people you're always pleased to see doing anything on television or in the theatre."
Shane Allen, the BBC's controller for comedy commissioning, said: "Richard Briers holds a very special place in British sitcom history having starred in several monumentally successful and well-loved shows. He was an incredibly accomplished actor who enjoyed a long, varied and distinguished career and will be greatly missed."
Penelope Keith called Briers' death "an enormous loss".
She told the Press Association: "I look back with enormous affection and love for Dickie. He was the most talented of actors, always self-deprecating. I learnt an awful lot from him during our time on The Good Life, over those 30 programmes.
"He was a wonderful mentor, tutor and teacher although that would suggest he imposed himself on you, which he didn't. He was always courteous and he would speak to the crew - which was not always that common.
"And he was always nervous. It was the most enjoyable time - when I think of The Good Life, I smile."
The actress, who also played opposite Briers in a TV adaptation of The Norman Conquests, went on: "He was a real gent - both gentle and a gentleman. He had this amazing body of work - successful television comedies, classics and West End plays.
"He is an enormous loss to our family."
The BBC's acting director-general Tim Davie said: "Richard Briers was one of our great BBC comedy actors, most memorably as Tom Good in The Good Life - still on our screens almost 40 years later, and still making us laugh.
"We'll miss his natural talent, both light and dark in later years, but his work will endure and, I am sure, bring lasting happiness."
Richard Briers: obituary
He was one of the most popular TV sitcom actors of his generation.
But Richard Briers was no less acclaimed as a distinguished Shakespearean actor, a major development in his career, at a point when he said "I realised I had gone as far as I could doing sitcoms".
He will be best remembered as a bumbling, fussy and occasionally downtrodden figure in some of the most successful TV comedies of his era.
He was the lynchpin of three of the most notable sitcoms ever made in Britain - Marriage Lines, The Good Life (shown in the United States as Good Neighbours) and Ever Decreasing Circles.
But after a long career in popular television, Briers joined Kenneth Branagh's Renaissance Theatre Company in 1987, and his already very successful professional life took a new turn as he moved on to major classical roles.
Briers was born on January 14 1934 and trained at the Royal Academy of Dramatic Art, where he won the silver medal and a scholarship to Liverpool Playhouse in 1956. Two years later he made his first West End appearance in Gilt And Gingerbread. He barely stopped working from that day onwards.
His big screen career began with the British features Bottoms Up (1960), Murder She Said (1961), The Girl On The Boat and A Matter of Who (both 1962) and the multi-national The VIPs (1963), followed by Raquel Welch's spy spoof Fathom (1967).
Over the next 36 years, he alternated his TV and film work with such plays as Present Laughter (1965), The Real Inspector Hound (1968), Butley (1972), Run For Your Wife (1983), Twelfth Night (1987-88) and A Midsummer Night's Dream (as Bottom, 1990).
Throughout these years, he was regularly and prominently on TV including such shows as Brothers In Law (1962), Bird On A Wing (1971), and starring with Michael Gambon in the series The Other One (1977).
Briers also provided the voice for the character of Fiver in the animated feature Watership Down (1978).
It was in 1987 that he joined Branagh's company, saying at the time: "Ken offered me Malvolio in his production of Twelfth Night at the very time I had decided to expand my career when I realised I had gone as far as I could doing sitcoms. As soon as I worked with him, I thought he was truly exceptional."
After his Malvolio, Briers took on King Lear at Branagh's insistence, followed by the title role in Uncle Vanya and Menenius in Coriolanus.
However, Briers still considered himself a sitcom clown, and on film Branagh cast him as Bardolph in Henry V (1989), as Stephen Fry's father in the comedy Peter's Friends (1992), Don Leonato in Much Ado About Nothing (1993), the blind grandfather in the controversial Mary Shelley's Frankenstein (1994) and as a cranky old trouper in A Midwinter's Tale (1996), the same year in which he filmed the role of Polonius in Hamlet.
He also co-starred with Sir John Gielgud in Branagh's Academy Award-nominated short film Swan Song.
It was his film-making with Branagh's company which made his name in the United States.
Other film credits included Michael Winner's A Chorus Of Disapproval (1989) and the big-screen version of the hit TV series Minder.
He also appeared in the harrowing period drama Skallagrigg (1994) and the PG Wodehouse comedy Heavy Weather (1996), with Peter O'Toole and Judy Parfitt.
Briers also often appeared in the works of the prolific playwright Alan Ayckbourn, playing leading roles in Relatively Speaking, Absurd Person Singular and Absent Friends on the stage and The Norman Conquests and Just Between Ourselves on television.
In recent years the actor saw his health deteriorate after being diagnosed with emphysema five years ago.
In an interview only a few weeks ago, he told how he blamed his years of smoking for the condition. "It's totally my fault. So, I get very breathless, which is a pain in the backside. Trying to get upstairs... oh God, it's ridiculous. Of course, when you're bloody nearly 80 it's depressing, because you've had it anyway."
He was awarded the OBE in 1989 for services to the arts. Briers married the actress Anne Davies in 1956. They had two daughters.