FRANKFURT/ZURICH, June 24 (Reuters) - French private equity group Astorg has agreed to acquire Swiss industrial software group Autoform for almost 700 million Swiss Francs ($721 million), people familiar with the deal said.

Germany's competition watchdog has already cleared the deal, according to a filing on its website.

Autoform, which makes software that helps carmakers to fashion sheet metal into new vehicles, was valued at about 19 times Autoform's expected earnings before interest, taxes, depreciation and amortisation (EBITDA), the people said.

Astorg and Autoform were not available for comment.

Autoform was founded in 1995 as a spinoff from the Swiss Federal Institute of Technology. It operates in a specialised niche of the broader field of industrial design known as "product lifecycle management" (PLM) led by names such as Autodesk, Dassault, PTC and Siemens .

Permira, HgCapital and TA Associates were runners-up in the auction, the people said. Reuters had reported in May that Autoform's founders had asked investment banking boutique Altium to find a buyer for the company. ($1 = 0.9714 Swiss francs) (Reporting by Arno Schuetze and Oliver Hirt; Editing by Georgina Prodhan)