The transfer fee for the midfielder is reported to be around £13 million. The 26-year-old had joined the Reds in 2012 and has played 91 league games for the club.
Stoke City confirmed the news of Twitter as well as on their official website. The tweet read:
After confirming their new signing, Stoke chief executive, Tony Scholes said:"Joe is a player that Mark 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.
"We have had to act swiftly to conclude the deal but we are delighted that we have managed to get it over the line."
Allen too spoke to the Stoke's official website and said: "It's been a whirlwind 48 hours for me but I am delighted to have finally been able to put pen to paper.
"I was really excited as soon as I heard of the Club's interest and it wasn't a difficult decision for me to make.
"I am incredibly excited about my future here at Stoke City."
Joe Allen will wear the number 4 jersey at Stoke City.