Briers had been battling the serious lung condition emphysema after years of smoking and died "peacefully" at his home in London on Sunday, the agent said.
The actor began his career in the theatre but won national fame in Britain in the 1970s for his role as Tom Good in The Good Life, a man who gives up his job at a plastics company to try his hand at self-sufficiency with his long-suffering wife Barbara, played by Felicity Kendal.
The show also aired in the US where it was retitled Good Neighbours.
Briers went on to star in the popular British sitcom Ever Decreasing Circles.
In later life he took on more film work and appeared in nine of British actor-director Branagh's films, particularly in Shakespearean roles, including in Henry V, Much Ado About Nothing and Hamlet.
Briers blamed smoking for his illness, in an interview published on January 31.
"The ciggies got me. I stopped 10 years ago, but too late," he told the Daily Mail newspaper.
"If you do it in your 30s, you're OK, but after 30 it gets you. I was diagnosed five years ago and didn't think it would go quite as badly as it has."