The 18-year-old had a medical with the Old Trafford outfit on Tuesday and was due to meet Sir Alex Ferguson on Wednesday to sort out his short-term future.
That could involve remaining at Old Trafford, or being allowed to leave on loan, either to an English club or his present team in Chile, Universidad.
United have yet to confirm details of the deal. However, speaking to Chile paper La Tercera, Henriquez touched on his bewilderment at the speed of the deal.
"I am super happy to get to Manchester United. I'm fulfilling a dream," he said. "I am going where I wanted. You look on television and see the outstanding players, scoring spectacular goals. I cannot waste this opportunity.
"It is not clear what will happen with my future. I want to play in the first team of Manchester United. That's my first thought. If they decide to send me on loan, I would prefer to continue at Universidad, although I will do whatever United deem appropriate."
- Sir Alex Ferguson
- Manchester United