The Greek defender, whose transfer fee reportedly costs £11.75 million, signed a long-term contract with the Premier League champions.
"I'm very happy, I'm very proud to be here. For me, (it's) the biggest club in the world," Tsimikas said. "It's an honor to be here, and I will give my best."
The 24-year-old will primarily compete with Andy Robertson for minutes in Jurgen Klopp's XI. Left-back was a weak position for Liverpool, with veteran midfielder James Milner among those regularly enlisted as Robertson's backup over the past couple of seasons.
The left-back emerged as the Reds' No. 1 target after the club balked at Norwich City's £20-million asking price for Jamal Lewis. Real Madrid's Sergio Reguilon, who's currently on loan at Sevilla, and Bournemouth's Lloyd Kelly were also potential recruits for Liverpool before they struck the deal for Tsimikas.
Tsimikas appeared 86 times for Olympiacos across all competitions. He won the Greek Super League this season and was part of the team that eliminated Arsenal in the Europa League round of 32.