Despite making just five first team appearances and scoring one goal for Atalanta, United forked out a reported £37m for the 18-year-old Ivorian in the January transfer window.
Diallo has joined the Red Devils on a four-and-a-half-year contract, with the deal having been agreed with the Serie A side back in October.
"I'm a little bit too anxious to say this given it's just the start [of my time here] but my dream is to win the Premier League and the Champions League with Manchester United. That is my aim and goal," Diallo said in a club interview.
"I'm over the moon to be here. I'm so excited to start here at Manchester United. It's a dream come true and I can't wait to start and play with the guys.
"It's been a little bit strange these last few months. I would have hoped to have played a little bit more with Atalanta, but it wasn't possible. Now I'm here and I'm very happy to be here and I'm expecting a lot from my experience here. I'm looking forward to starting."
Manchester United are three points clear at the top of the Premier League table ahead of this weekend’s meeting with champions Liverpool but have dropped down to the Europa League after finishing third behind Paris Saint Germain and RB Leipzig in their Champions League group.
