The 22-year-old Montenegro international – whose contract at Villa Park expires at the end of this month – has been in talks with Wolves for more than a month and a deal is almost done.
It is believed he will be sent out on loan next season to gain more senior experience.
Sarkic – due to be snapped up on a free transfer – has not played for Villa's first team, but he did impress during a loan spell at Scottish Premiership side Livingston in the first half of 2019/20.
He tweeted on Saturday night about his impending Villa exit, as he said: "What a journey! It’s been a great five years.
"Full of good memories and experiences. Thank you to all my team mates, everyone at the club and all the Villans!"
Sarkic has had a few offers on the table, but Wolves have always been his preferred destination.
Born in Grimsby to a Montenegrin father and British mother, he progressed through the youth ranks at Belgian side Anderlecht before joining Villa in 2015.
Since then, he has had loan spells at Wigan, Stratford Town, Havant & Waterlooville and, most recently, Livingston.
Sarkic made 18 appearances there before being recalled by Villa in January because of Tom Heaton's knee injury.
He made his Montenegro debut last November, in a 2-0 win against Belarus.