Gonzalez and Infante each had a $2.5 million option for next season. Infante would have received a $250,000 buyout if his option was declined.
Proctor gets a $750,000 contract, avoiding salary arbitration.
Atlanta turned down a $6 million mutual option on Ankiel, paying him a $500,000 buyout. The Braves declined a $5.25 million option on Farnsworth, who gets a $250,000 buyout. Both players became free agents.
The versatile Infante batted .321 and was selected to his first All-Star team this year.
Gonzalez was traded from Toronto to Atlanta on July 14. He had 23 homers and 88 RBI combined, and his 42 doubles led all major league shortstops.
The 33-year-old Proctor had a 6.35 ERA in 5 2/3 innings with Atlanta last season as he began his comeback from 2009 elbow ligament replacement surgery.
Proctor led the American League with 83 appearances for the Yankees in 2006, when he was 6-4 with one save and a 3.52 ERA.
Ankiel and Farnsworth had disappointing results after coming to Atlanta from the Royals. Ankiel, 31, batted .210 with two home runs in 47 games, though he did hit an extra-inning homer in San Francisco that sent the Braves to their only playoff victory this year.
Farnsworth, 34, was 0-2 with a 5.40 ERA in 23 appearances.
The Braves also reinstated right-hander Jairo Asencio to the 40-man roster.