The South Korea captain made the switch to Mainz on Saturday with Tuchel expressing his surprise at being able to realise such a deal.
"It's an extraordinary transfer for us," Tuchel told Kicker magazine. "We're very pleased about it and think Ja-cheol can improve us instantly.
"It's important to get players of his quality. He's going to do us good."
The 24-year-old signed a contract until 2018 with the current ninth-placed Bundesliga side, who are just four points adrift of a qualifying berth for Europe next season.
Koo spent 18 months on loan with Augsburg before returning to Wolfsburg last summer.
However, he struggled to make an impact with the Wolves and made just 10 appearances this season, most of them as a substitute.
"He's a very gifted, flexible player with outstanding technical qualities," Tuchel said.
"The way he plays football and his character make him a perfect fit for our team. I'm pleased that we've been able to pull off this transfer."