Cavani – out of contract at season's end – was tipped to leave PSG last month but a proposed transfer to LaLiga outfit Atletico Madrid did not materialize.
With an exit on hold until at least the end of the campaign, Cavani came off the bench and scored within three minutes of his introduction as PSG beat Ligue 1 rivals Lyon 4-2 on Sunday.
"Whenever there's competition it's good. We need all the players. I've always said that," Tuchel told reporters.
"You can feel that Edi [Cavani] is stronger in training at the moment because things are clear after the mercato. It's been like that for a few days now.
"He made a very good entrance [in the game], he put in a very important goal. It's good for him and for us. Because we need all the players with experience and quality like Edi. That's necessary. They are in good shape and that's good."
Cavani – PSG's all-time leading scorer – netted his third Ligue 1 goal of the season but first since August, while the Uruguay international forward has six across all competitions.