The Serbia international is expected to arrive on the south coast this morning for a medical examination at Bournemouth.
The two clubs have already agreed on a transfer fee of £25m.
Petrovic had a successful loan stint with Strasbourg last season and is set to become Bournemouth's new primary goalkeeper.
He will take over the position left vacant by Kepa Arrizabalaga, who spent last season on loan at Bournemouth from Chelsea before joining Arsenal a fortnight ago.
