The two clubs agreed a transfer in principle last month after the Reds reportedly met the release clause of the 20-year-old's contract at the German club.
"I am proud to be a part of the family and I am looking forward to playing here," Can told the club's official website. "I will give it my best.
"LFC is a great club and the fans are amongst the best in the world. I am looking forward to the first game and can't wait to step on the pitch for the first time at Anfield."
The German Under-21 international found the back of the net three times in 29 Bundesliga appearances last season.