Vallat, who had worked at Louis Vuitton and Christian Dior, was chief executive at Remy Martin before joining Richemont in June last year to put the fashion and accessories business back on track.
"Eric has been offered a wonderful opportunity outside the Group and I fully understand his decision to pursue it," Richemont Chairman Johann Rupert said in a statement on Tuesday.
Richemont has gone through several management reshuffles in recent years, reflecting difficulties at its watch unit and a stronger focus on online distribution that saw its technology chief throw in the towel in May last year.
Richemont declined to give further details on Vallat's departure.
The world's second-biggest luxury goods group generates the lion's share of its sales with Cartier jewellery and luxury watches sold under brands such as IWC and Vacheron Constantin.
Its fashion and accessories business, with labels such as Chloe, Dunhill and Montblanc, represented just 13% of group sales and suffered an operating loss in fiscal 2018/19 to the end of March.
Richemont sold struggling leather bagmaker Lancel to Italy's Piquadro last year.
Shares in Richemont were down 1.4% at 1045 GMT, lagging a 0.7% weaker sector index <.SXQP>.
(Reporting by Silke Koltrowitz, editing by Louise Heavens)