The two clubs agreed a deal in principle last month but the 20-year-old midfielder has now become Brendan Rodgers' third signing of the summer after Rickie Lambert and Adam Lallana, who both arrived from Southampton.
"I believe this season the team finished second in the league, so I want to be a Premier League champion next season," Can told the club's official website.
"It was an easy decision for me to sign with Liverpool as I had a very good chat with the manager, which clearly showed that the club and he wanted to sign me. This was important for me. I can say it was an easy decision for me."
Can, who has represented Germany at Under-21 level, began his youth career at Eintracht Frankfurt before moving to Bayern Munich at the age of 15.
Can made just six first-team appearances for the German champions before he was sold to Bayer Leverkusen but the midfielder maintains he learnt a great deal from his time at Bayern.
He added: "I am very thankful for my time at Bayern Munich, I played there for four years. It was a great honour to play for one of the biggest and best teams in the world.
"However, I am at Liverpool now and this is where my sole focus is. I believe Liverpool football club can be on a similar level to Bayern Munich next season.
"There were a couple of players [who influenced me]. At Bayern Munich, for example, there was Franck Ribery, who I got along with very well and who I have spoken with a lot. He obviously became European Footballer of the Year, hence there is a lot to learn from him on the training pitch.
"In my position especially, I also learned a lot from Bastian Schweinsteiger, Javi Martinez and Luiz Gustavo. They helped my development.
"I don't regret leaving Bayern Munich. I am convinced it was the correct step for me. I played a lot at Bayer Leverkusen.
"I played in the Champions League and in the Bundesliga. I have played a lot of games and it was a very good decision to go to Leverkusen. During the year, I matured and developed massively."