Financial details were not disclosed, but British media reported the deal was worth about 20 million pounds ($26.95 million) plus add-ons, surpassing Hull's previous record fee of 13 million pounds for Tottenham Hotspur midfielder Ryan Mason in 2016.
The 23-year-old won four Super League Greece titles with Olympiacos and was part of the side that won the UEFA Conference League in 2023-24.
Capped nine times by Greece, he was named Super League Greece Player of the Season in 2024-25.
"I am ready for a new chapter in my career... Hull City is something different because we are playing in the Premier League. We have to fight against top players, so it's a challenge for me. I feel ready," Tzolakis said in a statement.
Hull secured promotion to the Premier League by beating Middlesbrough in the Championship play-off final and begin their top-flight campaign at home to Manchester United on August 22nd.