The transfer was confirmed earlier today, with Allen signing a long-term contract after the Reds agreed to match his £15m release clause.
The 22-year-old midfielder has expressed his joy at joining such "a massive club", with whom he wants to enjoy some "great years".
"I feel incredible. Everyone knows the history of this club, it's a massive club, and I'm delighted to have joined," he said.
"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."
Allen will wear the number 24 shirt at Anfield, where he will reunite with former Swans manager Brendan Rodgers.