The Montenegro international arrives at Montgomery Waters Meadow as competition for the No.1 shirt with another former Wolves shot-stopper, Harry Burgoyne.
Sarkic, 23, made the move to Molineux from Aston Villa this summer, with Wolves keen to send him out on loan for first-team experience.
The Grimsby-born shot-stopper impressed last season on loan at Livingstone in the Scottish Premiership, where he made 14 appearances, including a 2-0 debut win against Celtic.
He has previously been on loan at Wigan – where he made three cup appearances – Stratford Town and Havant & Waterlooville. He is yet to make his debut in the Football League.
Sarkic, who stands at 6ft 5in, joined Wolves on a free transfer after his Villa Park contract expired this summer.
He becomes boss Sam Ricketts’ fifth new signing of the summer after Rekeil Pyke, Scott High, Josh Daniels and Marlon Fossey. Sarkic, whose twin brother Oliver plays for Blackpool. is a third loan signing.
Boss Ricketts said: “He’s a very good, young keeper who did really well last year at Livingston.
“We’re delighted to have him here at the club. He’s a really good prospect, Brian Jensen and myself are really looking forward to working with and he’s a great addition to the team.”
Sarkic is currently away on international duty with Montenegro – for whom he won his first and only cap last November – and will not feature for Salop at Middlesbrough in the Carabao Cup on Friday evening.
Academy graduate Cameron Gregory is well thought and will be on the bench at Boro. He will likely be loaned out again this season to experience more men's first-team football.
Town's new goalkeeper is the third full international in Shrewsbury's ranks after Grenada captain Aaron Pierre and Jason Cummings, who has played twice for Scotland.
He continues the link between Shrewsbury and one of Ricketts’ former sides Wolves. Town took Ryan Giles on a successful loan last season, before the Telford youngster was recalled and subsequently sent out to Coventry in January.
Sarkic was born in Lincolnshire but left for Brussels aged seven. He was eligible for England and Belgium but chose to represent the country of his father.
The keeper, a regular in the Montenegro youth set-up, spent time in the academy of Belgian giants Anderlecht before returning to England to join Villa’s academy aged 18 in 2015.