Telles, 27, has signed a four-year contract with the option for an additional 12 months, and arrives in a cut-price deal due to him having just one season left on his agreement with Porto.
"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," Telles said in a statement.
🔴 We have reached an agreement with Atalanta for the future transfer of Amad Diallo, subject to a medical, personal terms and work permit. 👋#MUFC— Manchester United (@ManUtd) October 5, 2020
"I won many trophies at 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."
Ole Gunnar Solskjaer said: "First and foremost, I welcome Alex to United. He is a player we have been tracking for some time and his performances over the past few years are exactly what we are looking for. He is a fighter and a winner and will add real determination and competition to the squad.
"Alex has the qualities, both as a player and as a person, that we want here at Manchester United."
💬 "I'm coming here to give my all."— Manchester United (@ManUtd) October 5, 2020
🤩 Alex Telles is buzzing for his next chapter at #MUFC, and you can hear more from our latest signing here 👇
United had been linked with Telles for a couple of weeks, with the club seemingly opting to go for him after reportedly refusing to agree to Real Madrid's terms in negotiations for Sergio Reguilon, who joined Tottenham.
Nevertheless, rumours of their interest in Telles and Reguilon did initially raise eyebrows due to the presence of Luke Shaw and Brandon Williams as United's left-back options.
But Shaw has long been criticised for a lack of attacking output, while Williams – who signed a new four-year deal in August – has failed to oust him.
It is hoped Telles will offer a greater source of flair and attacking prowess from the full-back position than United's previous options.
The Juventude academy product has created an average of two chances per 90 minutes in the Primeira Liga since the start of last season, while he has scored 13 goals and set up another 10.
While few would expect Telles to reach such figures in the Premier League, it highlights how effective he can be in the final third.
By comparison, neither Shaw nor Williams have registered an assist since the 2019-2020 Premier League season began, while the latter has a solitary goal and the former has none.
And in terms of chances created, Williams has averaged 1.2 key passes every game and Shaw just 0.9.
There were also serious questions raised of Shaw after Sunday's 6-1 humiliation at the hands of Tottenham, with the left-back partly culpable for at least two goals.