Salazar, who is coming off an inconsistent and injury-slowed 2017, will make $5 million next season. Chisenhall's contract is worth $5.58 million. He's projected to be the starting right fielder for the AL Central champions.
Cleveland also reached agreement with reliever Zach McAllister on a $2.45 million contract.
The Indians, however, didn't settle with Bauer before the deadline to exchange salary figures. The enigmatic right-hander won a career-high 17 games last season and developed into a vital member of Cleveland's rotation. He made 31 starts and established himself as a premier pitcher, known as much for his array of pitches as his hobby of flying drones or unique training regimen.
Bauer went 10-1 with a 2.60 ERA over the final two months of the season, when the Indians reeled off a league-record 22 straight wins and won their division title before losing to the New York Yankees in the AL Division Series.
Bauer's representatives submitted a salary of $6.25 million while the Indians countered at $5.3 million. Arbitrators will begin holding hearings on Jan. 29.
Earlier this week, the Indians avoided arbitration with closer Cody Allen, who will make $10.575 million next season.
Salazar went 5-6 with a 4.28 ERA and 145 strikeouts last season. But the right-hander spent time on the disabled list with elbow and shoulder injuries. Despite those issues, Salazar averaged 12.7 strikeouts per nine innings, second to Boston's Chris Sale (12.9) among pitchers with at least 100 innings.
Salazar is 38-33 with a 3.82 ERA in 188 starts for the Indians since 2013.
Chisenhall also struggled with injuries last season, spending time on the DL with a shoulder sprain, calf strain and a concussion. The former third baseman batted .288 with 12 homers and 53 RBIs in 82 games.