Tuchel arrived at Parc des Princes last year and guided PSG to a comfortable league title defence, but results were less impressive in the cup competitions.
PSG exited the Champions League to Manchester United in the last 16, while Guingamp inflicted an early Coupe de la Ligue exit and they were then beaten in the Coupe de France final by Rennes on penalties.
The shoot-out defeat to Rennes came in a run of just three wins in 10 matches in all competitions at the end of the season, concluding with Friday's 3-1 league defeat at Reims.
However, Tuchel insisted after the match that he was confident of remaining in Paris and news of a new deal – with a year-long extension – was confirmed on Saturday.
A club statement said Tuchel "won over the players, staff and the club with his natural warmth, as well as his modern vision of football".