The multi-year deal will see their logo on the left sleeve of City's first team, U23s and ladies shirts for all league games from the start of next season.
Other clubs have announced sleeve partnership deals but all with existing commercial partners. City are the first Club to strike a deal with a new brand.
Top Eleven, a mobile football management game launched seven years ago, has more than 160 million registered users and has been played in every country around the world.
It's the brainchild of Nordeus, an award-winning independent mobile games developer.
From the 2017/18 season onwards, Premier League clubs are entitled to have a secondary sponsor on one sleeve and the tie-up with Top Eleven does not affect bet365's main shirt sponsorship. Their logo will continue to adorn the front of the Club's shirt.
Stoke City Chief Executive Tony Scholes said: "Top Eleven are at the forefront of the football mobile games industry and they recognise the global reach that entering into a multi-year agreement with Stoke City gives them.
"We are delighted to become the first Premier League club to attract an entirely new commercial partner as Official Sleeve Partner and we look forward to a long and successful association with Nordeus and their Top Eleven football management game."
Nordeus CEO Branko Milutinović said: "We are really proud to partner with Stoke City, one of the oldest football clubs in the world. Top Eleven players build their club from scratch and have the opportunity to manage their team for years.
"We are one of the longest-lasting mobile football games on the market and we believe that Stoke City's long history through the football ages represents a story our millions of players will relate to."
The partnership was brokered by Lagardere Sports.
Visit the Top Eleven website at www.topeleven.com