Allen sealed a £13 million move to Stoke on Monday.
The Welshman sealed a £13 million move from Liverpool on Monday, and has become the club's second signing of the summer, following the arrival of Ramadan Sobhi earlier in the day.
Allen had largely struggled to hold down a first team place at Anfield under boss Jurgen Klopp, while a sparkling showing for Wales during their impressive Euro 2016 campaign heightened speculation linking him with a move away.
Former club Swansea City were seemingly favourites to sign the 26-year-old, but Stoke have now sealed a deal, with Allen signing a five-year deal at the club.
And Allen insists he is excited by the prospect of playing for City, adding that fellow Welshman Mark Hughes was a key factor in making his decision.
He told the club's official website: “He [Hughes] sold the club to me in terms of their ambitions moving forward.
"I wanted first-team football and for that reason it wasn’t too difficult (to move).
“I knew there was an opportunity like this here for me and it was easy to make the move.
“My ambition is to be a regular here and help Stoke City.
“They have been very stable in recent years and hopefully we can move upwards."
Allen arrives in the Potteries after being named in UEFA.com's Euro 2016 Team of the Tournament earlier in the summer, after playing a key role in the run that saw Wales reach the semi-finals.
He will be hoping to continue that good form for his new club, having largely failed to live up to the tag of the "Welsh Xavi" at Liverpool, a nickname bestowed on him by former boss Brendan Rodgers.