He also left a legacy of £10,000 to King’s College, Cambridge, where he studied English.
Bird, known for long-running Channel 4 satire show Bremner, Bird and Fortune, died at a care home in Midhurst, West Sussex, on Christmas Eve.
His fortune was left to stepsons Daniel and Josh, the children of his third wife Libby Crandon.
Bird and fellow satirist John Fortune won a Bafta in 1997.
They also collaborated with Rory Bremner on BBC shows Now, Something Else and The Rory Bremner Show.
Bird also appeared in the film Jabberwocky and TV comedies Yes, Prime Minister and One Foot in the Grave.
When Bird died Rory Bremner said: “It’s an irony that one of our greatest satirists, so brilliant at portraying ministers, civil servants or high-ranking officials who exuded self-satisfaction, was himself so modest and self-effacing.
“John Bird was, to the end, never pleased with himself, always feeling he should have done better, been less lazy, had a late period like Brahms, ‘where everything was spare and abstract’.
“The reality was that he and his friend and collaborator John Fortune, together with Peter Cook, were pillars of the anti-establishment.”