The goalkeeper left Eintracht in 2015 to join PSG, where he won Ligue 1 twice and was part of a treble-winning team in 2017-18.
However, he failed to establish himself as the undisputed number one keeper PSG hoped he could become and was loaned back to Frankfurt last season.
Trapp made 43 appearances in all competitions as the Eagles reached the semi-finals of the Europa League, losing on penalties to Chelsea, and finished seventh in the Bundesliga.
His performances convinced Eintracht to bring him back on a five-year-deal, and 29-year-old Trapp is confident that was the right move for him despite the club losing star forwards Luka Jovic and Sebastien Haller in the transfer window.
"I do not regret leaving Paris. I had a good time, but I deliberately signed in Frankfurt for five years," Trapp said ahead of the Europa League tie with Strasbourg.
"The club is developing in a very positive direction. I still have big plans for Eintracht.
"We agreed that I returned to PSG at the end of my loan but I was still in contact with the coach and several players. Then there were discussions between leaders and it was decided that I left again."