The 27-year-old, who has one cap for Brazil, moves to Old Trafford in a deal worth £13.6m plus £1.8m in add-ons.
Telles said: "To join a club with the prestige of Manchester United is a huge honour.
"You have to work hard to get to this moment in your career and now I am coming to this club, I can promise that I will give everything in my heart to be a success here.
"I won many trophies at FC Porto and I want to continue that at United. The manager has a clear plan and direction for this team and I can't wait to pull on the famous shirt."
Telles how you feel about our new signing...#MUFCpic.twitter.com/cYK2VFPKrd
— Manchester United (@ManUtd) October 5, 2020