The Reds will pay £125 million, with Isak forfeiting a £5 million loyalty bonus to help finalise the move.
An initial bid of around £110 million was rejected earlier in the window.
Newcastle told Liverpool in clear terms that Isak was not for sale, and the Reds backed off.
"I feel amazing. It’s been a long journey to get here. But I’m super-happy to be a part of this team, this club and everything it stands for. It’s something I’m proud of and I’m really looking forward to it," Isak told the club's website after the deal was announced.
"I’m just happy it’s done and that I can get back to work. I’m looking forward to seeing my teammates and the fans, and getting back out there."
The 25-year-old striker dug his heels in, though, and pushed for a move to Anfield, making a public statement.
In a post on Instagram, Isak said 'promises were broken' by Newcastle and 'the relationship can't continue'.
Following the signing of German striker Nick Woltemade for a club record £69 million, the EFL Cup holders were willing to meet Liverpool at the negotiating table.
Isak underwent his Liverpool medical in Kirkby on Monday after the clubs agreed a deal on Sunday night and signed for six years at Anfield.
The 25-year-old scored 62 goals in 109 appearances for Newcastle, with 54 of them in the Premier League. Last season, he finished behind Mohamed Salah in the race for the Golden Boot.
"I think I have a lot to give, I think I have a lot to improve. I’m a striker, but I always want to give as much as possible to the team, mainly goals, but much more than that as well," he added.
"I want to win everything."