The 23-year-old is expected to help lift Liverpool, who have drawn their first two Premier League matches this term, following Mohamed Salah’s departure at the end of last season.
Barcola passed his Liverpool medical over the weekend and is expected to provide the marquee signing the Reds were crying out for on the wings.
"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," Barcola was quoted as saying on the official club website.
"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," he added.
Barcola has signed a five-year deal with Liverpool and will wear the number 29 shirt.
He scored 39 goals in 152 appearances for PSG after joining the Paris club from old rivals Lyon in 2023, having worked his way through Les Gones' youth ranks.
PSG drove a hard bargain for Barcola, rejecting a £90m offer from Liverpool earlier this month. A saga followed, with the Parisians demanding as much as £145m, according to some reports.
The clubs ultimately settled on an initial £106m fee, with achievable add-ons potentially taking the total cost to just under £124m.
The reigning Ligue 1 champions have signed Maghnes Akliouche and Mika Godts this summer, potentially pushing Barcola down the pecking order in the French capital.
At Liverpool, Barcola is expected to slot into a familiar role on the left wing. Cody Gakpo has pretty much had that position locked down over the last 12 months, following Luis Diaz’s move to Bayern Munich, but the Dutchman is now expected to depart Anfield, with an eyebrow-raising transfer to Manchester City strongly rumoured.
Barcola won two Champions League titles with PSG, as well as three Ligue 1 crowns and two Coupes de France, among other honours.
As the summer transfer window ramps up, Flashscore has everything you need to keep up with breaking news, rumours and analysis. Follow our live transfer blog to follow the biggest moves, whilst expert Dean Jones will be on hand to provide the inside stories from around the world.