Back-row forwards Horstmann, 35, and Salvi, 31, have agreed one-year deals, while lock Atkins, 26, has extended his contract by two years.
Six team-mates, including Phil Dollman, Michele Campagnaro and Olly Woodburn, signed new deals last week.
"It's fantastic to have all three guys with us again next season," said Chiefs head coach Rob Baxter.
Exeter are currently second in the Premiership, six points behind leaders Wasps, and travel to face Leicester Tigers at Welford Road on Friday.
Exeter Chiefs trio Kai Horstmann, Julian Salvi and Ollie Atkins have signed new contracts with the club.