Havertz proved the Champions League final matchwinner and also shone for Germany over the summer.
Tuchel told the club's website: "For him personally he played a good Euros. He was a threat constantly in the German team for the others to score.
"Of course he had an excellent ending to our season and although the German team did not do so well at the Euros, I think he can personally be satisfied with the first steps he made here in England and with the outcome for him.
"There's things to improve, things to keep the level up high, where he can play and he proved that he can play. This is the next step."
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