Bruce was only appointed in January and did not actually take over for another month, guiding the Owls to a 12th-place finish in the Championship.
The Magpies held talks with Bruce, 58, on Saturday and he is the overwhelming favourite to succeed Rafael Benitez. He leaves Hillsborough with assistants Steve Agnew and Stephen Clemence.
Newcastle have flown to China without a manager as they prepare to face Wolves in the Premier League Asia Trophy in Nanjing on Wednesday.Born near Newcastle and a boyhood Magpies fan, Bruce told BBC Radio Sheffield on Sunday: “Speculation is speculation. It’s in the hands of the clubs. For me, there’s nothing to talk about until the two clubs reach some sort of compromise.” During his career, Bruce has managed 10 clubs, including a spell in charge of Newcastle’s north-east rivals Sunderland.
Benitez left the Magpies at the expiry of his contract at the end of last season, and has said the Premier League club “did not share his vision”.