Mowbray said: “I’ve got an opportunity to steer us back to where we want to go and that is towards the Premier League.
“Our ambition is to get the club moving back in the right direction.”
Mowbray guided West Brom into England’s top flight in the 2007-08 season and has been out of work since his contract was terminated by Celtic in March.
The 46-year-old, who captained Boro and made 424 appearances for the club during his playing career, admitted he did not think twice about accepting his former side’s offer.
“Since I was six or seven I’ve been a Boro fan and once the opportunity arose and a few things were ironed out it didn’t take me a moment’s thought,” Mowbray continued.
It is the second time Mowbray has replaced Strachan in a management post – the new Boro boss took over from the Scot at Celtic Park in the summer of 2009.
Meanwhile, Boro legend Bernie Slaven launched a scathing attack on Strachan following a dismal record of just 13 wins in 46 games.
“After a year in charge, we had not improved one iota – the football was average, away results were abysmal, the worst league position in 20 years and he still doesn’t know his best team,” said Slaven, 49.
“It wasn’t just on the field that Strachan let himself down, off the field during post -match interviews he became an embarrassment to himself, the club and the fans.
He added: “He was arrogant, obnoxious, sarcastic, cutting and rude. He came across to me like a man who was on the borderline of insanity.”
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