"I would like to apologise on behalf on [sic] Monty Python for all the many sketches we did making fun of white English people," Cleese said.
"We're sorry for any distress we may have caused."
In another tweet, Cleese, while discussing so-called "woke-ism", said: "Started out as a good idea – 'Let's be nice to people' – and finished up as a humourless, censorious, literal-minded, posturing idiocy."
Apu was a much-loved fixture in The Simpsons, but criticism emerged in 2017 that the show's producers had for decades relied on offensive stereotypes.
Apu was "sidelined" and Azaria announced last January that he would no longer voice the character.