AFC Bournemouth had their bid accepted by the Blues, worth a reported £25million in total.
The keeper will now travel to complete the move, and will have a medical at the Cherries in the week, the Daily Echo understands.
Petrovic comes in as another Chelsea keeper, loanee at Dean Court last season Kepa Arrizabalaga, returned to London from the Cherries, before being sold to Arsenal for £5m.
Kepa played the majority of the games last season for Andoni Iraola's side, as the clear number one in the squad, although Mark Travers impressed when called upon in the first half of the season.
But Travers sought regular game time, leaving to join Middlesbrough on loan in January.
Travers, Neto and Alex Paulsen all returned from their loan moves this summer, and with the signing of Petrovic likely to be concluded, one or more of those keepers may depart, be that on loan or in permanent deals.
Everton are reportedly interested in the Irishman, with David Moyes a fan of the keeper.