, both players will join their respective clubs on loan with views to permanent transfers.
Bruce has long been an admirer of Mido and finally got his man after Boro agreed to let him go on the condition King would move in the opposite direction.
For King, the move is ideal, having failed to settle at the JJB Stadium. He was at Hull on loan but returned after reportedly falling out with Phil Brown.
Mido's move to Wigan has fuelled speculation that Emile Heskey will sign for Liverpool before the January transfer window closes.
Meanwhile, Bruce has warned Chelsea and Manchester United that they have no chance signing midfielder Antonio Valencia.
Wigan have already sold Wilson Palacios to Tottenham, for a fee believed to be worth around £14 million, subject to the Honduras international receiving a work permit.
As such, Bruce is determined not to lose another influential midfielder, and said: "I am the manager of a club that is always going to lose our better players when the big boys come in.
"But I won't be losing two players this month, this for sure."