Brendan Rodgers revealed on Thursday night that a deal was imminent after the Wales international attended the club’s Europa League match against Gomel at Anfield.
The transfer has now been finalised to allow Allen to complete a move to Merseyside, where he will be reunited with his former manager at Swansea.
Liverpool’s pursuit of the 22-year-old has dragged on for much of the summer and Allen is now relishing the prospect of trying to make an important contribution for his new club.
“I feel incredible. Everyone knows the history of this club, it’s a massive club, and I’m delighted to have joined,” he told Liverpool’s official website.
“I feel incredible. Everyone knows the history of this club, it’s a massive club, and I’m delighted to have joined.”
“The passion that people here have for football is something I share and I want to be part of that.
“I’m looking forward to being part of some great years ahead for Liverpool Football Club.”
Rodgers is also thrilled to have secured the services of a player whose style was so influential in helping Swansea earn such rave reviews last season.
Rodgers said: “I’m absolutely delighted that Joe has made the decision to come with us on this journey.
“Joe is a player whose profile will fit perfectly with the ideas of this group. His ability to control and dominate the ball is an important ingredient in our attempt to gain success on the field.
“Joe has had a fantastic education at Swansea City and will now begin the next chapter in his exciting career, and I wish him all the very best in what I’m sure will be a long and distinguished career here at Liverpool.”