Johnny Beattie, Sydney Devine and Glen Michael were among around 300 hundred people who attended the service at the Auld Kirk in Ayr to say a final farewell to the 77-year-old who died last weekend.
Jack was one half of the Alexander Brothers, and with his sibling Tom played across the world and recorded more than 30 albums in a career that spanned 50 years.
Originally from Cambusnethan in Wishaw, they started performing on stage in the 1950s in a series of talent contests across central Scotland with Jack playing the piano and Tom on the accordion.
They won every competition they entered between 1950 and 1956, according to their fan club biography, and started playing professionally in 1958.
Many of the mourners at the Kirk wore tartan, inspired by the Alexander Brothers' traditional stage outfits, and the funeral cortege was accompanied by three flower arrangements; a giant thistle, a piano and a treble clef.
During the service songs recorded by Mr Alexander, including Come In, It's Nice to See You and Farewell My Love, were played.
His wife Lillian wrote a poem to her husband that was read by the Rev David Gemmell.
It said: "You'll never stop singing; we'll still hear your voice, From painter to artist - you made the right choice.
"You know we all love you - especially me; Rest in peace my darling husband, Jack Alexander MBE."
Mr Alexander's grandchildren also wrote a poem to their "Papa Piano" and read it out during the service.
Mr Beattie did the eulogy and started by saying: "You've done it again Jack, another full house.
"He would have appreciated that, and it really is great seeing everyone here because it's a celebration of Jack's life, it was a very fulfilled and happy life."
The actor and entertainer went on to describe how he first met the Alexander Brothers.
He said: "I was doing a summer show in North Berwick in 1954 and I'd never heard of the boys, but I was walking in Dunbar and there on a big bill on the gable end of a building it said 'Eddie Williams presents Tom and Jack, the fabulous Alexander Brothers, direct from the Cafe de Paris', so I did some investigating and it turned out the Alexander Brothers were two painters from Cambusnethan and the Cafe de Paris was an ice-cream shop in Wishaw.
"I said, 'I don't even know these boys but I think I'm going to like them', and sure enough we went on to be great friends.
"They didn't act like big stars, it was just such a joy, such a delight to know them. Jack will never be forgotten, Lil knows that and all the family and our presence here today says it all.
"He'll be so sadly missed but certainly never be forgotten. Thanks for the memories Jack."
Mr Alexander suffered a brain haemorrhage last month and was being treated in the Ayrshire Hospice, Ayr. He died peacefully with his family around him on Saturday.
Rev Gemmell said: "He was one of Scotland's best-known and well-loved entertainers. For over 60 years he entertained people not just in Scotland but all over the world with his musical talent.
"He played Carnegie Hall in America, Sydney Opera House in Australia and even outsold the Beatles. Not bad for a wee boy from Wishaw."
The Alexander Brothers first album was titled Highland Fling, and they went on to tour Canada, the United States, Australia and New Zealand.
Their recording of Nobody's Child in 1964 is said to have sold more copies in Scotland than any Beatles song in that year.
They were both awarded MBEs for services to entertainment in the 2005 New Year Honours List.
After the funeral service Glen Michael, who performed with the brothers on stage before he started a career in children's television, said: "My memories of Jack are so pleasant, I'd just bought a new car and turned up for a show in Dundee I was doing with Jack Milroy and he was there with his brother. They all liked the car and helped me wash it to keep it looking nice.
"That's what he was like, he was so down to earth. I'm sure if he had been alive today he would have a had a giggle because the atmosphere inside the service was more like a theatre and he would have loved that."
Another contemporary of Mr Alexander was singer Sydney Devine.
He said: "Jack was such a nice person, a showbiz legend and he'll be sadly missed in Scotland by fans and the people he worked with.
"It's another icon that has disappeared from our stages and screens."