The 53-year-old was named as United’s new manager on Friday morning ending months of speculation linking the former Inter Milan and Real Madrid boss to the Old Trafford position.
The Red Devils finished in fifth place in the Premier League table behind Manchester City on goal difference meaning a second season in three years without Champions League football.
Mourinho has been out of football management since December when Chelsea sacked the Portuguese coach following the west London side’s dismal start to the defence of their Premier League crown.
And Carrick, whose future at Old Trafford is uncertain, backed Mourinho to bring back success to the 20-time English champions following his much-anticipated triumph.
“Mourinho’s track record speaks for itself. He’s a good fit for the club and hopefully he’ll do very well,” Carrick told Sky Sports.
“I have to say it’s sad to see anyone lose their job – the manager and staff – but good times are ahead.”
United won the FA Cup thanks to a 2-1 extra-time victory over Crystal Palace at Wembley thanks to Jesse Lingard’s winner at the home of English football.
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