Glasgow-born Mr Marr, who presents The Andrew Marr Show on BBC 1, fell ill on January 8, but will continue his recovery at home, where he will undergo a physiotherapy regime.
The 53-year-old, who has received messages of support from across the political spectrum, is expected to return to work later this year.
A BBC spokeswoman said: "Andrew Marr left hospital earlier on today and continues his rehabilitation at home with his family.
"He says thank you to all the wonderful nurses, doctors and physiotherapists at Charing Cross hospital [in London] who have looked after him so well.
"He is looking forward to a new regime of physio at home as he prepares for his return to work later this year."
She added that Marr and his family hope people will allow him to recover privately.
The broadcaster is married to journalist Jackie Ashley and has three children.
Guest presenters, including Jeremy Vine, have stepped in to cover his duties since the stroke.
A BBC series about Scottish writers was put on hold while the presenter made his recovery, although pre-production work on the project, due to air in spring 2014, continued.
Marr, the corporation's former political editor, began his career as a newspaper reporter in Scotland. He moved to London and was part of the team that launched The Independent newspaper in 1986.
He later became editor of the paper before turning to television, joining the BBC as political editor in May 2000.
Marr is best-known for presenting BBC One's Andrew Marr Show and Radio 4's Start The Week.
He has also presented a number of history programmes along with his politics show and has had five books published.
The presenter suffered the stroke at home just after New Year. He has since said that goodwill messages had been "truly wonderful" and sent out a "huge thank you" to well-wishers.
According to Radio 4 sources he had been "hungry for news from outside" when he was in hospital and had taken radio recordings to entertain him.
Around 150,000 people in the UK suffer from a stroke every year – accounting for one every five minutes.
Strokes affect people in different ways and outcomes are largely dependent on how quickly the patient is treated.
It occurs when the blood supply to part of the brain is cut off. Symptoms of a stroke include numbness, speech problems and weakness of paralysis on one side of the body.
Strokes mainly occur in people over the age of 65, but they can occur at any time.
Marr is a keen distance runner but he said that in his past he had smoked and had a few years of hard drinking.
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