Shane Allen, BBC controller of comedy commissioning, said Perry's work spanned decades and his shows will be remembered for a long time to come.
He said: "Jimmy Perry is a Goliath of British comedy writing. He was behind some of the longest running and most loved sitcoms on British television spanning the 60s, 70s and 80s.
"His work will be enjoyed and appreciated for many years to come. Our thoughts are with his friends and loved ones at this sad time."
'Allo 'Allo star Vicki Michelle said Perry had left "such a legacy" in his wake.
She tweeted: "So sad we have lost Jimmy Perry a brilliant comedy writer & true gentleman.
"He leaves us such a legacy."
Michelle has said she considered Perry, Croft and 'Allo 'Allo writer Jeremy Lloyd "largely responsible for the golden age of British comedy".
