Isak was signed by Liverpool for a record £125m from Newcastle United on deadline day.
The Swede told the club's website: "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.
"It’s mixed emotions – some relief but a lot of pride, happiness. 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.
"I feel like this is the next step for me in my career. I’m super-happy that I’ve been given this chance and I’m very motivated to do something well with it."
Asked about why he chose Isak, he also said: "I think it’s a mixture of what the club is building, but what they’re building on top of what the club already is. The history of the club. Me getting the chance to be a part of this, I want to create history. I want to win trophies. That’s ultimately the biggest motivation for me and I feel like this is the perfect place for me to grow even further and to take my game to the next level and help the team as well.
"It has been a long summer but I’m just looking forward, not looking at the past. It’s done now and I know I can get back to doing what I love the most. Really looking forward to it."
Isak will wear Liverpool's No9 shirt and insists he's be available for their next game at Burnley after the international break.
"Yeah, of course, I think that’s the ambition. However, I’ve had a tricky summer where I haven’t played any games and I’ve had restricted training, so I think that’s one to judge and to analyse where I am at and how much I am ready to give. But I certainly want to play as soon as possible."