Zimbabwe-born Armand, 28, joined the Chiefs from Super Rugby side Stormers in 2013 and has since played 55 Premiership games, scoring six tries, and represented England Saxons.
Hill, 22, has made 12 league appearances for the Chiefs since moving from Gloucester in 2015.
The pair are among 11 Chiefs players to re-sign beyond this season.
In addition, Chiefs have signed Gloucester flanker Matt Kvesic, Bridgend winger Tom O'Flaherty and Rotherham forward Toby Salmon, and others could follow.
"We are really pleased," head coach Rob Baxter said. "We are very close to completing the signing of a high-quality player, and we will probably be able to announce that in the next couple of weeks.
"We are still actively in the market for potentially one more high-quality player."
Back-rower Don Armand and lock Jonny Hill have signed new contracts with Exeter Chiefs that will expire in 2019.