Kottas began playing basketball with the youth teams of APS Ajax Amynteo. He then transferred to play with the youth teams of PAOK Thessaloniki in the summer of 2011. After playing with the junior teams of PAOK Thessaloniki, Kottas began his professional career in 2013, with the senior men's team of PAOK. He left the club after 3 years, due to his limited playing time.
On 27 August 2020, Kottas signed with Larisa.[4] In 21 games, he averaged 3.4 points and 3.1 rebounds per contest. On 26 July 2021, Kottas signed with Aris, returning to Thessaloniki.[5] In 24 games, he averaged 2.7 points, 2.4 rebounds and 0.6 blocks in under 10 minutes per contest.
On August 29, 2022, Kottas signed with Karditsa. On November 3 of the same year, he moved to Romanian club CSM Târgu Jiu for the rest of the season.
On September 5, 2023, Kottas moved to AEK Athens.[6] His contract was terminated on December 11, 2023.[7] On the same day, Kottas signed a two-year deal with Iraklis.