Swanson agreed at $3.15 million and Foltynewicz at $6,425,000. Also reaching deals were outfielder Adam Duvall ($3.25 million), right-hander Luke Jackson ($1,825,000), infielder Johan Camargo ($1.7 million) and left-hander Grant Dayton ($655,000).
The team did not reach an agreement and now faces arbitration with right-hander Shane Greene, who was 0-1 with a 4.01 ERA in 27 games with Atlanta after a midseason move from Detroit, where he was the closer. Greene has filed for a salary of $6.75 million, while Atlanta has offered $6.25 million.
Swanson, who hit a career-high 17 homers despite missing 30 games with a right foot contusion, agreed to a $3.15 million deal for the 2020 season. He earned a big raise from $585,000.
Foltynewicz, who revived his career last season following a demotion to Triple-A Gwinnett, earned $5.5 million in 2018 and enters spring training as one of the top four starters in a rotation that has added Cole Hamels.
The 27-year-old was 8-6 with a 4.54 ERA last season. Atlanta won each of his 12 starts from June 11 through Sept. 20. Despite his resurgence, Foltynewicz ended his season by giving up six runs in his second Division Series start, recording only one out in the decisive 13-1 Game 5 loss.
Jackson lost the closer's job last season, but it was still a breakout year for the right-hander, who earned a raise from $585,000. He averaged 13.1 strikeouts per nine innings and posted a 3.84 ERA in 70 games.
Duvall could open the season in a left field platoon with Nick Markakis. Duvall hit 10 homers in 41 games with Atlanta following his recall from Triple-A Gwinnett, where he hit 32 homers. He earned $2,875,000 last season.
Duvall's power potential could be especially important if the Braves can't re-sign free agent third baseman Josh Donaldson.
Donaldson's decision also could be important to Camargo, whose production declined in a utility role in 2019, when he had a $575,000 salary. He hit 19 homers and drove in 76 runs in 2018, when he was the primary third baseman.
Dayton posted a 3.00 ERA in 14 games while earning $585,000 in his comeback from Tommy John surgery.