Matic is one of several new faces at Old Trafford for 2018-19, alongside Romelu Lukaku and Victor Lindelof.
The United manager knows him well, the pair having worked together at Chelsea in a spell that brought the 2014-15 Premier League title to Stamford Bridge.
And it was his arrival that most pleased Mourinho ahead of what will be a big season for the Red Devils.
"I could see when I first came to United that we needed a Matic-type player," he told reporters in Saturday's press conference.
"But there are not many around and I do not like to go after players where it is an impossible mission. Then I heard that he wanted to join United and could make it happen.
"I am very happy to have him because he is one of those players with no question marks. He doesn't need time to adapt. He’s not a young guy coming from another country. He’s just turned 29 and he has five years' Premier League experience. He gives me something I really like which is consistency. He is a fantastic signing for us because I can trust him to perform at a high level.
"He is a fantastic signing."
Mourinho's first season at Old Trafford saw United finish sixth in the English top flight, though they won the Europa League and EFL Cup.
He confessed to reporters that he is relishing the pressure to improve in the upcoming Premier League campaign, which kicks off against West Ham on Sunday.
"The only thing I have to do is work every day like I always do, the only demand on me is the one I put on myself," Mourinho said.
"I don't put any extra pressure on myself because I always give everything, then normally the results are a good consequence of that work. My dedication to my job is always at the maximum, even more now than when I started, and I believe at the end of the season we will see the results.
"With these players I am looking forward to the season with optimism, with enthusiasm, I can't wait for the Champions League to start and the chance to play the top clubs. I am on fire."