Trapp left Frankfurt in 2015 for PSG but has struggled to earn a starting spot in the last two seasons in France.
The arrival of Italy great Gianluigi Buffon at PSG further hampered the German's chances of regular playing time.
The Germany international, who was part of their World Cup squad in June, played 96 matches in all competitions for Frankfurt from 2012-15.
He was signed after Frankfurt keeper Frederik Roennow was ruled out for a lengthy period with a knee injury.
"We now had a chance, with Kevin, to sign a goalkeeper who not only was ready to play instantly but also an identity figure with great leadership potential," said Frankfurt sports director Bruno Huebner.
Frankfurt, who won the German Cup last season, won their Bundesliga opener last week and host Werder Bremen on Saturday.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
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