Dalot, tipped to be a long-term replacement for Antonio Valencia, has agreed a five-year contract that will keep him at Old Trafford until 2023, with the option of a further 12 months.
"Joining Manchester United is an unbelievable opportunity for me," Dalot told ManUtd.com.
"I have grown up in Porto's Academy and I am so thankful for everything they have done for me. But the chance of coming to the biggest club in the world is something I just couldn't turn down.
"I'm excited about working with Jose Mourinho and learning everything I can from such a successful coach. I am looking forward to playing alongside the fantastic players in the squad."
Mourinho, who shares the Porto connection with Dalot, said, "Diogo is an extremely talented young defender with all the qualities to quickly become a great player for this club
"In his age group, he is the best full-back in Europe and we all believe he has a bright future ahead of him at Manchester United."