The transfer, subject to international clearance, sees Liverpool pay an initial £106m with a further £17m available in add-ons, making Barcola the second-most expensive signing in the club's history behind only Alexander Isak.
He signed his deal at the AXA Training Centre after passing a medical, and will wear the number 29 shirt he also had at PSG, with the contract running until 2031.
"It's a great pride to be able to play for Liverpool. I'm very happy," Barcola told Liverpoolfc.com.
"It took a long time but I'm really happy today to be able to play for Liverpool and all I want is to be on the pitch and be able to play.
"I hope to achieve very big things. First of all, winning the Premier League - it's one of my biggest dreams in my life. It is to do that and to stay in this team in the long term - that's why I signed a long contract - and I hope I can do it."
Barcola arrives after three years at PSG, where he made 152 appearances, scored 39 goals and provided 35 assists, winning back-to-back Champions League titles and three consecutive Ligue 1 titles along the way. He first broke through at Lyon, making his senior debut in November 2021 and contributing seven goals and 11 assists in 47 appearances before a £39m move to PSG in August 2023.
On the international stage, he has won 28 caps for France since his debut in June 2024, scoring six goals - three of them at this summer's World Cup, where he was ever-present as France finished fourth.
Reflecting on what drew him to Anfield, Barcola pointed to prior experience of the stadium's atmosphere.
"I had the chance to play twice in this stadium and I saw the atmosphere and how the fans were behind the Liverpool players," he said. "When I knew about Liverpool's interest in me, I didn't ask questions and I knew it was a very big club for me."