The Bundesliga side announced the boss signed a new contract at the beginning of the week, which is set to see him stay for another season
The 52-year-old had previously been linked with a move to Schalke, but club CEO Heribert Bruchhagen expressed his delight of securing Veh's services for at least another year.
"I am very happy that we were able to create continuity in the sporting aspect," the 64-year-old club chief was quoted as saying on their official website.
After arriving at the Commerzbank Arena in the summer of 2011, Veh led the team to promotion to Germany's top flight in his first season.
The former Hamburg boss then added to this success this season and Frankfurt are currently flirting with a Champions League football spot as they occupy the fourth place in Bundesliga as of late March.