The 23-year-old striker has signed a five-and-a-half-year contract after the Club agreed a guaranteed fee of £12million with West Bromwich Albion. The fee could rise to £15million based on player and Club success.
Berahino is the Potters' second signing of the January transfer window after Lee Grant's loan switch from Derby County was made a permanent arrangement and ends a long-time pursuit of the former England Under-21 international.
City Chief Executive Tony Scholes told stokecityfc.com: "It's no secret that we have been looking to bring Saido to the Club for a long time and to suggest that we are pleased to have finally concluded the deal is an understatement.
"We've signed a young English striker who has already proven his ability in the Premier League.
"After a frustrating period he's now desperately keen to reignite his career and we look forward to seeing him do that with us."
Berahino, a product of Albion's youth system, scored 23 league goals in 105 appearances for the Baggies after loan spells earlier in his career with Northampton Town, Brentford and Peterborough United.
He's unavailable for City's meeting with Manchester United at the bet365 Stadium tomorrow but he is expected to be in the crowd for the sell-out clash.