Tsimikas agreed a five-year contract with Liverpool and is expected to provide back-up for first choice left-back Andy Robertson at Anfield.
Reds boss Jurgen Klopp moved for the 24-year-old after opting not to pay Norwich's asking price for their Northern Ireland left-back Jamal Lewis.
Tsimikas is Liverpool's first close-season signing and he told the club's website: "I'm very happy, I'm very proud to be here. For me, (it is) the biggest club in the world. The league here, I like a lot. I watch it on the TV and it was always one dream I had from when I was a kid to come to play in this league. (I want) to achieve (our) goals. To win the league again and also to win the Champions League."