Veh, who replaces Thomas Schaaf in charge, has agreed a two-year??deal with the Bundesliga club.
“Eintracht Frankfurt was and will continue to be a very special challenge for me,” Veh said.
“I will try everything to guide the team into a positive future.”
Veh was in charge of Eintracht from 2011 to 2014, leading the club to promotion back to the top flight and then to Europa League qualification.
He left a year ago to join VfB Stuttgart for a second spell but lasted just 12 matches before resigning with the the club in the relegation zone and having been knocked out of the German Cup in the first round.
Under Schaaf, Frankfurt finished a respectable ninth last season.