He's been given the green light by United to make his Wigan debut against Bournemouth in the FA Cup third round this weekend.
"This is a fantastic opportunity for me and I am really excited after the manager has given this chance for me to prove myself," Henriquez said.
"Now I need to work to try and earn my place in the Wigan team."
Latics boss Roberto Martinez was delighted at securing the services of a centre-forward with Arouna Kone preparing to jet out next week for the African Nations Cup.
"We're really excited about Angelo because he is a very young man with a huge potential," gushed Martinez.
"He's a goalscorer with clever movement inside the box, and has had a very successful time in Chilean football.
"We hope to have a good partnership in terms of allowing Angelo to develop as a footballer and learn of the demands of the English game, because I feel he can bring us something different in the forward line.
"I'm sure the fans will give him a great welcome on Saturday, and it will provide him with the perfect opportunity to begin his experiences on the pitch in English football which is very exciting."