Speculation has been mounting over the 'Price Tag' star's future involvement with the show since May, with a report last week claiming that she was definitely out.
O'Donoghue is quoted by The People as saying: "I'm really sad she's not coming back - we have a great friendship."
Defending his coaching partner, the Script singer added: "She wasn't a diva at all - I have never seen her throw tantrums.
"Jessie is incredibly articulate and she's headstrong. That sometimes can be misconstrued as being too arrogant. But she's a brilliant role model for young women."
Sir Tom Jones recently revealed that he was in talks with the BBC about renewing his contract, but stated that he would only do so once he knew the identities of the three other coaches.
There have been no official confirmations so far, but O'Donoghue and will.i.am are both expected to retain their places on the panel.
Watch Jessie J perform with her final act Vince Kidd below: