The South Korea international signed a four-and-a-half-year deal on Saturday after an undisclosed fee had been agreed with former club Wolfsburg.
Koo has made 10 appearances in the league this season after impressing while on loan at Augsburg for the previous two campaigns.
The attacking midfielder has only scored eight league goals since arriving in Germany in 2010, but he hopes to improve on all aspects of his game at the Coface Arena.
Speaking after his first training session with his new team-mates, Koo admitted it might take him time to get up to full fitness, but he was delighted to have made the move.
"The body and legs are a little tired, but my head and heart rejoice," he said.
"I have wanted to come to Mainz for a long time.
"I have seen almost every game on television, my friend Park Joo-Ho has said that the atmosphere within the team is very friendly.
"I have often heard that the team is a great team, that the club has good fans.
"I'm looking forward to playing here, (and) want to get better (as a) player."
Koo's first opportunity to impress for his new team, who sit ninth in the German top flight, will come on Saturday at Stuttgart.
