According to The Sun, the Geordie striker, 25, agreed to the move yesterday.
The Whites signed Bridges from Sunderland for £4.5m four seasons ago and he scored 21 goals in a total of 62 appearances.
Newcastle had agreed to take Bridges on loan before Mark Viduka’s departure for Australia to see his ill father.
They have since resurrected talks with Leeds and the player, whose contract expires at the end of the season, is thought to have structured a deal to sign until May.
Toon boss Bobby Robson has been a long-time admirer of the striker.