Luts began playing football at Flora youth academy in Paide. He made his Flora – and Meistriliiga – debut on 4 October 2008, coming on as a 72nd-minute substitute for Sergei Mošnikov in a 1–1 draw against Tallinna Kalev at A. Le Coq Arena. Luts scored his first Meistriliiga goal on 1 November 2008, in a 4–2 home win over TVMK. In July 2009, he joined Tulevik on loan until the end of the season.
Luts became a regular starter for Flora in the 2010 season, in which he scored 6 goals in 31 games and won his first Meistriliiga title.[2] He won his second Meistriliiga title in the 2011 season.[3]
IFK Norrköping
On 22 January 2013, Luts signed a two-year contract with Allsvenskan club IFK Norrköping.[4] On 4 April 2013, his missed penalty in the shoout-out against Djurgårdens IF saw IFK Norrköping eliminated in the quarter-finals of the 2012–13 Svenska Cupen. Luts made his debut in the Allsvenskan on 8 April 2013, in a 2–1 home victory over Gefle IF.[5] He made 13 league appearances in the 2013 season. After missing first half of the season due to injury, Luts was released by the club in June 2014.[6]
Levadia
On 16 January 2015, Luts signed a one-year contract with Meistriliiga club Levadia.[7][8] He made his debut for Levadia on 3 March 2015, against Santos in the Estonian Supercup, winning the match 5–0.[9]
Luts made his senior international debut for Estonia on 17 November 2010, replacing Tarmo Kink in the 76th minute of a 1–1 home draw against Liechtenstein in a friendly.[14] His first goal for Estonia on 7 June 2014, in a 2–1 friendly victory over Tajikistan, brought him the Estonian Silverball award for the best goal scored for the national team in 2014.[15][16]
On 28 March 2017, Luts scored his second international goal after just 58 seconds in a 3–0 friendly victory over Croatia.[17]