The actress - who portrayed the dim but lovable Alice Tinker opposite French's Geraldine Granger in the long-running BBC comedy - died of natural causes on Wednesday evening, her agent confirmed.
Doncaster-born Chambers also starred as Hugh Grant's ditsy sister Honey in Richard Curtis' Bafta-winning film 'Notting Hill'.
"Emma was a very bright spark and the most loyal & loving friend anyone could wish for," French said in a statement to the Press Association:
"I will miss her very much."
Emma Chambers, second row, in the now famous film 'Notting Hill'. Source: AAP
Recalling their characters' close friendship, French shared a photo of Alice lying on top of Geraldine in a shot from the popular series.
She wrote on Twitter: "I was regularly humped like this by the unique & beautiful spark that was Emma Chambers. I never minded. I loved her. A lot."
Grant called news of her death "very sad".
"Emma Chambers was a hilarious and very warm person and of course a brilliant actress," he wrote on Twitter.
Each episode of The Vicar Of Dibley would close with Geraldine telling a joke to Alice who would either react nonplussed, interpret it literally, or only understand the humour once it was explained.
Former 'Top Gear' presenter Jeremy Clarkson, who grew up in Doncaster near Chambers, wrote: "I'm sad about Emma Chambers.
"Knew her when she was a kid in Doncaster. She was very funny."
Chambers' agent John Grant said in a statement: "We are very sad to announce the untimely death, from natural causes, of the acclaimed actress, Emma Chambers.
"Over the years, Emma created a wealth of characters and an immense body of work.
"She brought laughter and joy to many, and will be greatly missed.
Jon Plowman, executive producer of 'The Vicar Of Dibley' and former head of comedy at the BBC, said: "This is a sad day. Emma was a gifted comic actress who made any part she played - no matter how ditzy or other worldly - look easy.
"To create a much-loved comic character as she did, you have to be every bit as bright and clever as Emma always was.
"She was great fun to work with and adored by all the cast and crew of 'Vicar Of Dibley'. She will be missed and our deepest condolences go out to her family and friends."
