Assigned the No.17 shirt, Nawrocki becomes Brendan Rodgers's fifth signing during the summer transfer window and the third addition of the week, following the arrivals of South Korean duo Yang Hyun-jun and Kwon Hyeok-kyu.
"It's great for me to have joined Celtic and I'm looking forward to meeting up with my new teammates and start training with them," Nawrocki told the club's official website.
"Celtic are a famous club throughout the world and, of course, they're very well-known in Poland, having had a number of Polish players in recent years, so I know just how big this club is and how incredible the supporters are, and I can't wait to play in front of the fans and experience that for myself."
Rodgers added:
"It's another very good signing for us and we're delighted to have brought Maik to the club.
"He's a very highly-rated young player and someone who we believe will be a great addition to the squad.
"He's also a player I am very much aware of, having seen him play for Legia Warsaw in the Europa League and I know he was very keen to move to Celtic, so we're looking forward to working with him."