Helen Thomas, head of Radio 2, added: “I’d like to thank Paul for so many years of his brilliant Sunday afternoon show.
“I’m sorry to see him go, but I wish Paul the very best of luck for the future and hope to work with him again as the door is always open to him here at Radio 2.”
In February, after the schedule change prompted an unhappy response from listeners, the BBC said plans “evolve over time”.
“Paul is much-loved by many of our listeners, and whilst we’re making this change to Sunday afternoons, he very much remains a firm favourite here in Wogan House,” it said.
The presenter, also known by his drag queen persona Lily Savage, told his Instagram followers the arrangement with Mr Beckett was “nothing to do with me”.
Mr O’Grady launched his weekly show in the Sunday time slot in 2009.
His final show will feature his regular features, including Lost TV Theme, the Thank You Letter Of The Week and an unexpected playlist.
The BBC confirmed Mr Beckett will return for at least another 13 weeks of shows from Sunday August 21.
