The 20-year-old Serbia international becomes Derek McInnes' 11th signing of the summer, arriving with experience across three countries despite his age.
Nedeljković joined Aston Villa from Red Star Belgrade in January 2024 but managed only 10 appearances across all competitions before two separate loan spells at Bundesliga side RB Leipzig, the second of which ran through the whole of last season.
"Kosta is an athletic and energetic full-back who is keen to get forward, but he also has a real desire to defend and compete, and he will further strengthen a key area for us," McInnes told the club's official website. "He has already gained some valuable experience at a high level in England and Germany, as well as representing Serbia internationally."
Reports on the exact terms of the obligation have varied, with figures cited between £4m and roughly €4.5m depending on the outlet, though multiple sources agree the buy clause is tied to appearances rather than being unconditional. Rangers have prioritised right-back reinforcements this summer following the departure of former captain James Tavernier, with Dujon Sterling and Ross McCrorie currently sharing the role.
Nedeljković made his Premier League debut for Villa against West Ham United in August 2024, becoming the 1,000th player to represent the club, but limited game time pushed him toward regular loan spells in Germany instead. He was capped at various Serbia youth levels before beginning to draw interest from the senior set-up.
"Rangers is such a big club, a big family, and I am excited to join and help the team have success together," Nedeljković said.
"For me, it was an easy decision after meeting with the coach; I only wanted Rangers. It is a big opportunity and a big responsibility. I always try to be positive and work hard."
His countryman Vanja Dragojević, who joined Rangers from FK Partizan earlier in the window, is understood to have played a part in persuading Nedeljković to move to Glasgow rather than pursue interest elsewhere. McInnes personally called the defender on multiple occasions over the summer, according to reports in England, as Rangers pushed to get the deal done before their Scottish Premiership fixtures resume.
Villa had signed Nedeljković for a reported fee in the region of €7.6m from Red Star, where he came through the youth system and helped the club to a domestic league and cup double while remaining on loan there for the second half of the 2023-24 season.
With competition for places at right-back intensifying at Villa Park, the club opted to sanction a permanent-track exit rather than risk a third season of limited opportunities for the defender.