Born in Ribeirão Preto, Brazil, Koutris started his career from a local amateur team from Rhodes, Niki Rodos, where he was spotted by Super League club Ergotelis scouts in 2011. On 28 January 2013, he signed his first professional contract with the club and made his debut as a substitute in a match against Greek champions Olympiacos on 1 December 2013. Already an international with the Greek U19 and U21 squads, and considered one of the greatest talents at Ergotelis, he renewed his contract with the club on 5 June 2014. After Ergotelis' relegation to the Football Leaguein the summer of 2015, and despite reported interest from Greek giants Panathinaikos, Koutris was one of the 17 players to hold out as part of the club's roster until the very end, which came in January 2016, when Ergotelis officially withdrew from professional competitions, and released all players from their contracts.
On 25 July 2017, he made his debut with the club in a 3–1 away win UEFA game against Partizan. He played all the international games of the club, helping Olympiacos to reach UEFA Champions League group stage, after a year. On 9 September 2017, he made his debut with the club in the Super League in a 1–1 away draw against Xanthi. According to various sources, Eintracht Frankfurt and Benfica keep a close eye on Olympiacos' left-back. The Greek giants are aware of the interest in his services and they are eager to hand him a new contract. On 18 November 2017, he scored his first goal with the club, sealing a 2–1 home Super League game against Levadiakos. He was voted MVP of the game. On 15 November 2018, according to various reports West Ham United sporting director Mario Husillos spent the international break watching Leonardo Koutris as the club line up a move for a new left back. Koutris made his debut in Greece’s Uefa Nations League victory over Finland, a game that Husillos personally attended. West Ham manager Manuel Pellegrini has identified left-back as one of the areas he would like to strengthen, having not been convinced by either Arthur Masuaku or Aaron Cresswell. On 9 January 2019, Olympiacos rejected an official bid of Italian club Genoa for the Greek international at the range of €5 million.
On 29 January 2020, Koutris signed a six months contract with La Liga club Mallorca, on loan from Olympiacos. On 15 February 2020, he made his debut the club as a substitute in the first half, replacing Lumor Agbenyenu in a 1–0 win home game against Deportivo Alavés. On 21 February 2020, Koutris will miss the next six months after receiving the dreaded anterior cruciate ligament injury in La Liga. The Greek international suffered the injury in the 31st minute of a 3–3 home match against Real Betis.
Koutris holds both Greek as well as Brazilian citizenship, being born of a Greek father and a Brazilian mother.
Stretcher bearer incident
On 17 October 2015, during an Ergotelis game vs AEL at the AEL FC Arena for the Greek Football League, Koutris was involuntarily involved in a comical incident after having gone down injured by a challenge just outside the penalty area. Unable to stand up, Koutris was roughly loaded onto a stretcher by two stretcher bearers, who proceeded to drop him twice while carrying him outside, before unceremoniously dumping him at the side of the pitch. Ergotelis issued a formal complaint a few hours after the match had ended. The incident video went viral worldwide, and received coverage from major networks, such as BBC and the Telegraph, as well as being shown on The Ellen DeGeneres Show.