The France international completed his long-pursued move from Paris Saint-Germain in a deal worth an initial £106 million, rising to £123 million with add-ons, making him the second most expensive signing in Liverpool's history behind only Isak and just ahead of Florian Wirtz.
The 23-year-old has already made two appearances for his new club, offering glimpses of what he can bring to Andoni Iraola's attack after one of the summer's longest-running transfer sagas.
Isak, who arrived at Anfield from Newcastle for £125 million last summer, said he was excited about linking up with his new teammate.
"It's obviously an important signing for us, and he's a fantastic player who we're all familiar with because of his previous performances," Isak told the club's official website.
"I'm sure he'll help us become a much better team. So we're really looking forward to it."
Barcola made his home debut in the Champions League win over Atletico Madrid in midweek, having previously come off the bench during Liverpool's Premier League victory at Ipswich.
Isak's own first season at Liverpool was disrupted by injury problems and a difficult, acrimonious build-up to his move from Newcastle, and he scored just four goals in all competitions as a result. He has started this campaign strongly under new head coach Iraola, who succeeded Arne Slot over the summer, and has already netted three goals in three Premier League appearances.
"It's obviously been challenging, especially with all the injuries," Isak said. "But there have also been good moments, times when I've learned a lot. I see all of this as something that helps me become better and stronger; I don't look back too much, I just focus on what's ahead of me."
The Sweden international also thanked supporters for their patience during a difficult debut year on Merseyside.
"The support from the Liverpool fans means a lot. I've obviously known and seen how amazing the fans at this club are," he added.
Barcola, who has signed a five-year contract, had been Liverpool's top transfer priority throughout the window and was determined to leave Paris, having won three Ligue 1 titles and two Champions League crowns during his time at the Parc des Princes.
He also scored three times for France at this summer's World Cup, having netted 39 goals and provided 35 assists across 152 appearances for PSG in all competitions since arriving from Lyon in 2023.