Craig, 48, is said to have turned down a £68 million offer from MGM Studios to return to 007 for two more films after 2015’s Spectre.
Last year the actor joked to Time Out that he would rather “slash my wrists” than play the British Secret Service agent again.
He told studio bosses returning to the role “just wasn’t what he wanted” despite them throwing “huge amounts of money at him”, a source told the Daily Mail.
“Daniel is done — pure and simple — he told top brass at MGM after Spectre,” the source said.
He added: “He had told people after shooting that this would be his final outing, but the film company still felt he could come around after Spectre if he was offered a money deal.”
The source said that a knee injury he suffered during filming for a scene in Spectre had helped him decide that “it was a journey with an ending”.
A flurry of bets at the end of last week tipped The Night Manager star Hiddleston to replace Craig as the spy with the licence to kill, making him the 2-1 favourite.
After a big gamble, his odds plummeted to 1-2 and Coral bookmakers suspended betting on Saturday.
Last week Hiddleston was reportedly spotted meeting with Bond film director Sam Mendes and producer Barbara Broccoli.
Luther star Idris Elba and Homeland actor Damian Lewis had been frontrunners for the job in previous months, Coral said.
Elba was priced at 9-1 and Lewis at 14-1 before betting was suspended. Poldark star Aidan Turner had 3-1 odds and Mad Max: Fury Road actor Tom Hardy was at 4-1.
Craig, who is married to actress Rachel Weisz, has played Bond in four films in the franchise — Casino Royale, Quantum Of Solace, Skyfall and Spectre.
The movies have made more than £2 billion in box office revenue and Craig is reported to have been paid a total of £38m.