Petrovic joins the club on a five-year contract for a fee of £25million in total, arriving on the south coast having spent last season on loan at Strasbourg in Ligue 1.
The Serbia international starred while in France, winning the club’s player of the season as Le Racing finished seventh and qualified for the UEFA Conference League.
Petrovic told afcb.co.uk after completing the move: “I’m really happy to be here.
“I came to Bournemouth because I want to grow and I want to play at the best level. Together with this club, with these facilities, I think we can achieve it.
“I want to help the team get the results, improve every day and be a better player.”
The 25-year-old began his career at Serbian club Čukarički in Belgrade, rising through the club’s youth ranks and making his first team debut in 2019 in the Serbian top flight after a loan to third tier side FK IMT.
After 78 appearances for the Serbian side, Petrovic moved to the MLS, joining New England Revolution in 2022.
Here, he became the fastest player to make five penalty saves, before joining the Blues in August 2023, for a reported £12.5m plus add ons.
He made his Premier League debut as a substitute in December of that year, replacing the injured Robert Sanchez at Everton.
He started the following game as Chelsea beat Sheffield United 2-0, before he saved a penalty in the shootout against Newcastle to send the London side through the Carabao Cup semifinals.
In total, Petrovic has made 23 appearances for Chelsea in the Premier League, keeping five clean sheets.
Last summer, Petrovic headed to France to fellow BlueCo-owned club Strasbourg, playing 31 times in the French top flight.
He joins the Cherries after Kepa Arrizabalaga returned to Chelsea this summer following his successful loan at Dean Court, the Spaniard joining Arsenal.
Bournemouth have sold keeper Mark Travers this week to Everton, with the move confirmed on Tuesday.
AFC Bournemouth’s president of football operations, Tiago Pinto, told the club website: “I’m really pleased to bring Djordje to the club.
“The opportunity to sign a player of his calibre in the market was one we had to take, particularly given how vital the position of a goalkeeper is.
“We have been looking for the right talent to invest in within this area of the pitch and Djordje has very impressive qualities, as well as a lot of experience for someone who is still young. We are excited that he is the one coming to join our project and look forward to working with him.”
Petrovic is the second signing for the Cherries this summer, after the arrival of Adrien Truffert from Rennes.