Paul Bhattacharjee, 53, was last seen leaving the Royal Court theatre in London's Sloane Square on 10 July.
His body was found at Splash Point cliffs in Seaford, East Sussex, on 12 July. It was confirmed on Wednesday that it was the actor.
Next of kin have been informed. Police said his death was not being treated as suspicious.
The actor, from Redbridge, north-east London, was said to be in good spirits when he was last seen but after sending a text message to his girlfriend at 21:00 BST, no-one heard from him and an appeal was launched.