Exeter, who finished sixth in the Aviva Premiership in the 2012/13 season, have yet to confirm the signing.
The 24-year-old Maritzburg College flank failed to get regular game time for the Stormers this Super Rugby season, but was instrumental in Western Province's 2012 Currie Cup final triumph over the Sharks.
"It's been an amazing privilege to be a part of the Stormers family," the blindside flank tweeted.
"My team-mates, management and especially the fans have given me an amazing experience. Memories that will last a lifetime."
Armand joins the growing exodus of Stormers players seeking to forward their rugby careers overseas, including Bryan Habana (Toulon), Andries Bekker (Kobelco Steelers), Dewaldt Duvenage (Perpignan) and Joe Pietersen (Biarritz).