The Chile under-23 striker joins United from Universidad de Chile for an undisclosed fee.
Sir Alex Ferguson is delighted with the news and told ManUtd.com: “Angelo has made a tremendous impact on the game in his short career so far. His pace is a great asset and he reads the game really well for someone of such a young age.
"We have a proud record of developing young talent and Angelo fits the profile of a United player – skilful, attacking and someone who plays the game with real flair.”
Henriquez himself is equally excited at the prospect of pulling on the red shirt: “I am thrilled to be joining the biggest club in the world. Manchester United is a great team and has a great manager.
"To be able to be part of that is a huge honour and I can’t wait to get started. I hope I can be part of many successful years with United.”
Henriquez's squad number for the 2012/13 campaign will be no.21.
More: The Gossip - September