Bruno put pen to paper on a five-and-a-half year contract, with an option to extend for a further year, a statement on United's official website said.
The 25-year-old Portuguese international has contributed 63 goals and 52 assists in 137 appearances for Sporting Clube de Portugal. He has made 19 senior appearances for his country and was part of the successful squad that won the UEFA Nations League in 2019.
"My love of Manchester United really started when I used to watch Cristiano Ronaldo play and ever since then I have been a big fan of this great club.
"For me to now play for Manchester United feels incredible, I have worked hard to get to this moment and I can promise the fans that I will give everything for the badge to help bring us more success and trophies.
"I want to thank Sporting for everything they have done for me. It is surreal to hear the nice words that have been said about me from players that used to play for this team. A massive thank you to Ole and everyone at Manchester United for the trust they have shown in me and I can't wait to start to repay that on the pitch," Fernandes was quoted as saying by www.manutd.com.
United manager Ole Gunnar Solskjaer said: "We have been tracking Bruno for many months and everyone here has been tremendously impressed with all his attributes and what he will bring to this team. Most importantly he is a terrific human being with a great personality and his leadership qualities are clear for all to see."
"Bruno's goals and assists stats speak for themselves, he will be a fantastic addition to our team and he will help us push on in the second part of the season. The winter break is coming at a perfect time for us to integrate Bruno into the squad and for him to get to know his team-mates," Solskjaer added.
( With inputs from IANS )