The 20-year-old completed his switch to Anfield today after agreeing a move last month.
"Emre is an exciting young talent and I'm delighted he's chosen Liverpool for the next phase of his development and growth as a player," Rodgers told the club's official website.
"We have tracked his progress for some time and I have been impressed with his attitude and qualities when I have seen him play both in the German Bundesliga and the Champions League.
"He has many of the attributes we look for - charisma on the football pitch and courage to want the ball and make things happen."
Can scored three times in 29 appearances in the Bundesliga last season.