Should he pass a medical, Depay will become United manager Louis van Gaal's first signing of the summer after the Red Devils agreed to pay 22 million pounds for the 21-year-old.
Despite Paris Saint-Germain and Liverpool also expressing their interest in Depay, the Netherlands international revealed that he had no hesitation in choosing to make the switch to United.
"It was an exciting and pretty hectic period, and to have a choice between so many top clubs doesn't make it any easier," Depay told his agency's website. "For me, Manchester United is an absolute dream club, so I didn't need any convincing of the guys who already play at Manchester United. They told me only positive things, though."
The winger added that he is excited to be playing alongside his Dutch team-mates Robin van Persie and Daley Blind, and added that he couldn't wait to work with Van Gaal once more.
"I'm looking forward to playing with my Dutch team-mates next to all the other great players of Manchester United, and working with manager Louis van Gaal again is also a big bonus," he said.
Depay, who scored 21 goals to help PSV retain the Dutch title this season, also made it clear that his decision to sign with United was not motivated by money.
"In the end it was just a matter of feeling, not a matter of money," he said. "I've learned so much at PSV, not only on the pitch but also as a person. That makes me grateful, but I really felt it was time for me to move on.
"And you can't deny the interest of a club like Manchester United. I'm proud of winning the title with PSV. It's something the fans deserved, and something I wanted so bad as well."