Vlachodimos started his career with local club VfL Stuttgart-Wangen. He later joined VfB Stuttgart in 2001. He was promoted to the reserve team in 2010. On 20 June 2011, Vlachodimos moved to Greek Superleague club Skoda Xanthi. He made his debut for the club on 28 August 2011 against PAOK. He scored his first goal against Panathinaikos, his next goal came against Olympiacos in a stunning 1–0 victory against the Greek giants, he scored his third and final goal of the season against PAS Giannina. For his efforts during the season, he won the best young player award for the 2011–12 season. On 23 May 2012, Vlachodimos signed a five-year contract with Greek side Olympiacos for a transfer fee of €400,000. He made his debut on 20 October 2012 against his former club Skoda Xanthi in a 4–0 home win. In a Greek Cup match against Panachaiki, Vlachodimos assisted Kostas Mitroglou's goal in a 2–0 home win. On 14 February 2013, he also made his European debut against Levante in a 3–0 away loss. In the second leg against Levante of the Europa League, Vlachodimos made an impressive performance but it was not enough to save Olympiakos from being knocked out on a 4–0 aggregate. Three days later, Vlachodimos assisted Giannis Maniatis's goal in a 2–1 win over Aris on 24 February. His first goal came one week later in Olympiakos's 4–0 away win over OFI. He also managed to score against Platanias in a 4–0 away win. On 6 July 2013, Vlachodimos joined Bundesliga side FC Augsburg on a season–long loan. He made his first and only appearance for Augsburg on 10 August 2013 against Borussia Dortmund. At the end of the year, the club cancelled his loan and he returned to Greece. In January 2014 he signed for Platanias on loan from Olympiacos until the end of the season. On 2 February 2015, Vlachodimos joined French Ligue 2 side Nîmes Olympique for the rest of the 2014–15 season. On 30 August 2015, after having returned to Olympiacos, his contract was dissolved and Vlachodimos became a free agent. On 5 January 2016, it was announced that Panathinaikos had a deal with Vlachodimos, who was released by Olympiacos the previous summer and had been training with Greuther Fürth and Arminia Bielefeld. Eventually, on 6 January 2016, he signed with "The Greens". On 30 January 2016, despite the probable legal actions for the signing of the player from Olympiacos, he was included in Panathinaikos' squad for the leagueaway match against Platanias. Eventually, on 10 February 2016, he made his debut with the club in a 1–0 away loss against Atromitos for the Greek Cup coming in as a late substitute. On 14 February 2016 he made his debut in the Super League, opening the score in a 3–0 away win against PAS Giannina. On 10 July 2017, Vlachodimos signed for French Ligue 2 side Nîmes Olympique on a three-year contract, after not being in the plans of Panathinaikos coach Marinos Ouzounidis. On 27 August 2017, he scored his first goal with the club sealing a 1–0 home win game against Le Havre AC. At the end of the season, he returned to Ligue 1, for the first time since the 1992–93 season after finishing second in Ligue 2. On 23 August 2019, Vlachodimos joined Sonnenhof Großaspach on a two-year deal.
International career
Vlachodimos decided to represent Greece, the country of his origin, from youth level. He has played for the under-19 team and the under-21 team.
Personal life
Panagiotis is the older brother of Odysseas, who plays for S.L. Benfica in Portugal.