According to Sky Sports, the fee for 28-year-old Martinez could rise to £20m (€21.6m) with add-ons.
Martinez is due to undergo a medical with Villa this weekend, although is still to agree personal terms.
Reina has since returned to AC Milan and joined Lazio, forcing Villa into the market for a new goalkeeper.
Heaton is due back in the near future but will face stern competition from Martinez from now on.
Martinez joined Arsenal from Independiente as a teenager and has spent a decade with the Gunners.
Emiliano Martinez’s move from Arsenal to Aston Villa has now been made official.
🇦🇷 @EmiMartinezz1 🇦🇷
— Aston Villa (@AVFCOfficial) September 16, 2020