Veh, whose previous deal was due to expire in June, had been strongly linked with a move to Schalke, whose director of sport Horst Heldt was a player of his during the 2007 Bundesliga-winning season together in Stuttgart.
Veh had remained coy about his future and was hoping to announce a decision after his side reached 40 points for the season, a figure which theoretically equates to safety.
However, a haul of just two points in the last five games have kept Frankfurt below that 40-point mark and Veh has decided instead to use the international break to conclude contract negotiations with the club.
"I'm very pleased that we have managed to realise continuity in our sporting aspects," said the club's president Heribert Bruchhagen in a statement on the Bundesliga club's website.
Veh will officially put pen to paper at a press conference tomorrow having given the club his word.
Veh took over in Frankfurt 18 months ago and led them to promotion from the second division last season.
They currently lie fourth in the table, on course for a place in Europe next season with eight games of the season remaining.