The 28-year-old has been linked with a move to Stamford Bridge for much of the summer after Petr Cech departed for Arsenal, with the Bosnia international now providing competition for Thibaut Courtois.
Stoke, who signed experienced goalkeeper Shay Given last week, tweeted confirmation that Begovic had made the move on Monday afternoon, while Chelsea also confirmed the transfer.
The fee for Begovic is undisclosed, but Chelsea are believed to have paid around £8million for the keeperm, who had one year remaining on his Stoke contract.
“I am very happy to be joining Chelsea. After speaking at length to the manager, I feel like I can develop here and be an important part of this team. I am looking forward to meeting up with the team on Wednesday for the pre-season tour,” tweeted Begovic.
The 28-year-old established himself as the first-choice goalkeeper at the Brittania Stadium having moved from Portsmouth in 2010, winning the Stoke player of the year award in 2013.
Having been capped 41 times by Bosnia, Begovic has the experience and Premier League know-how to challenge Courtois for the goalkeeping berth in Jose Mourinho’s side.
He issued a statement via Twitter thanking everyone at Stoke for his five years with the club and is ready to challenge himself with the champions.
“I would like to say thank you to everyone at Stoke Football club, the chairman and the Coates family, Mark Hughes and Tony Pulis, goalkeeper coach Andy Quy, all my team-mates and especially the fans who have made me and my
family so welcome,” he wrote.
“I have loved my time at Stoke, but feel I had to take this opportunity for me to contine to develop and challenge myself as a player.
“I am very proud of what we have achieved during my time at Stoke, and it has been a great team of players to work with. I wish you all the best for the season ahead.”
Cech left Chelsea for London rivals Arsenal, with Begovic – who the Blues confirmed will wear the number one jersey – the second big summer arrival at Stamford Bridge following the loan signing of Monaco forward Radamel Falcao.