Ash was Barrick Gold's CIO for three years until the end of 2018.
It is unclear if she'll continue as chair of the Global Mining Guidelines Group.
Ash has worked in the mining and manufacturing industries for more than 20 years and was named in the 2016 list of "100 Global Inspirational Women in Mining" by Women in Mining UK.
"Michelle will help shape strategy to build growth across the Natural Resources sector, as well as deliver next-gen solutions based on [Dassault's] 3DEXPERIENCE [software]," Dassault said.
Paris-headquartered Dassault is a global software company that bought Gemcom at the height of the last mining boom, underpinning its new Geovia natural resources arm.