The 24-year-old moves to St Andrews having spent last term at Shrewsbury, where he played 29 games.
“I am delighted to be here and have settled in really well with the lads,” said Sarkic.
“I know a few of the boys already from previous clubs so I am really happy to be here and have settled in nicely.
“I got the shout that the gaffer wanted to look at me and I said yes straight away because I back myself.
“It was an obvious decision for me to come and show what I can do, and it has paid off.”
Sarkic was snapped up by Wolves in the summer of 2020 having been released by Villa.
The Montenegro international had a successful spell at Scottish club Livingston in 19/20.
“I think of myself as a goalkeeper as someone that has a lot of presence, I like to command players around me and my box,” added Sarkic.
“I also like to play with my feet and helping out players when they need it.
“I want to be a positive impact on the team and help us get plenty of positive results.”