The Reds last week accepted Stoke’s bid of up to £13m for their midfielder, whose performances helped Wales reach the semi-finals at Euro 2016 this summer.
And the 26-year-old has signed a five-year contract, ending a four-year spell at Anfield to become Stoke’s second arrival of the summer following Ramadan Sobhi’s move on Monday.
“It’s been a whirlwind 48 hours for me but I am delighted to have finally been able to put pen to paper,” Allen told his new club’s website.
“It wasn’t a difficult decision for me to make. I am incredibly excited about my future here at Stoke City.”
Stoke chief executive Tony Scholes said: “Joe is a player that Mark Hughes has admired for a considerable amount of time.
“Therefore when we became aware of the possibility of bringing him to the club it was something that we were determined to do.”
Allen followed Brendan Rodgers from Swansea to Liverpool in 2012 but found his first-team chances limited after Rodgers was replaced by Jurgen Klopp in October.
Injuries contributed to a total of just eight Premier League starts last season, and Allen had just one year to run on his deal.
He will wear the No 4 shirt at Stoke.