Mbappe's Bosman move was confirmed earlier this week, with the transfer to be officially rubberstamped on July 1.
"It's a fantastic feeling, it's a dream come true. I am extremely proud to come to a club that I have always dreamed of," he said.
"I come here with great humility. There are a lot of emotions."
Mbappé also took the opportunity to speak out about last season at PSG - where the striker says that he was first told by the club that he would not play anymore, after making the decision to leave.
"I was told that I would no longer play for PSG. It was said straight to my face, so I was convinced that I wouldn't play anymore," he said.
"Luis Enrique (coach) and Luis Campos (director) saved me. Without them, I wouldn't have stepped out onto the field again."