The Portuguese coach signed a three-year contract with the Red Devils on Friday after days of speculation linking him with the Old Trafford job.
Mourinho had been out of work since his sacking by Chelsea back in December following the west London club’s disastrous season.
Terry remains a keen admirer of Mourinho and is backing the former Real Madrid and Inter Milan boss to bring success back to United in the seasons to come.
Speaking to Sky Sports, Terry said: “It’s fantastic news for Manchester United.
“I’m sure that United’s fans and players will be delighted with that because, as I’ve said many times before, he’s the best manager I’ve worked under.
“It was unfortunate the way it ended at Chelsea this year but I wish him well because he’s also a great man. He’ll be great for Manchester United, I’m sure.”
Mourinho is already believed to be working on his plans for the summer transfer window as he bids to restore United to the top of English football.
His appointment came just days after the Red Devils opted to sack Louis van Gaal following the club’s fifth-placed finish in the Premier League table.
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