The Mets declined their option on injured pitcher Johan Santana, while Boston exercised its option on pitcher Jon Lester.
Toronto exercised options on closer Casey Janssen, first baseman Adam Lind and infielder Mark DeRosa and declined an option on infielder Munenori Kawasaki.
Jeter, who turns 40 next June, was limited to 17 games this year after breaking his ankle in the 2012 playoffs. He spent four stints on the disabled list in the most frustrating season of his 19-year career. His deal had included a $9.5 million player option.
Across town, the Mets declined a $25 million option on Santana and will pay the two-time Cy Young Award winner a $5.5 million buyout. Santana, who turns 35 on March 13, went 46-34 with a 3.18 ERA while with the Mets, missing the 2011 and 2013 seasons because of shoulder injuries.
Lester, who gets $13 million, was the starting and winning pitcher twice during Boston's six-game World Series victory over the St. Louis Cardinals. The 29-year-old was 15-8 with a 3.75 ERA in the regular season. He went 4-1 with a 1.65 ERA in the post-season, including victories in Games 1 and 5 of the Series.
Nathan, the Texas Rangers' All-Star closer, declined his half of a $9 million mutual option. The pitcher, who turns 39 this month, was 6-2 with a 1.39 ERA and 43 saves last season and wants a multiyear deal.
"My expectation is that there are other teams that maybe have a bigger need in the bullpen and will put in more resources than we are," Rangers general manager Jon Daniels said. "We have some other areas that are a higher priority for us to address."
Detroit declined a $3.25 million option on Veras, who receives a $150,000 buyout. The 33-year-old was 0-5 with a 3.02 ERA in 67 appearances with the Astros and Tigers this year.
Janssen will get $4 million from Toronto, Lind $7 million and DeRosa $750,000. Kawasaki, whose option price was $1 million, does not receive a buyout.
Jimenez became a free agent after the Indians picked up his $8 million club option and he exercised his right to void it.
After going 9-17 in 2012 and leading the AL in losses, Jimenez went 13-9 with a 3.30 ERA this season, including 4-0 in September. The Indians can make him a $14.1 million qualifying offer by Monday, and he would have a week to accept. If he declines, the Indians would receive a 2014 first-round draft pick if he signs with another team.
Also, the Indians declined their $7.5 million club option on outfielder Jason Kubel. He was acquired from Arizona on Aug. 20.
Oakland exercised its $7.5 million option on centre fielder Coco Crisp, who hit a career-high 22 home runs in the leadoff spot. The A's also exercised its $8 million option on left-hander Brett Anderson and declined an $8.5 million option on catcher Kurt Suzuki and an $11 million option outfielder Chris Young. Young gets a $1.5 million buyout and Suzuki $650,000.
Seattle declined a $7.5 million option on Gutierrez and a $7.9 million option on left-hander Joe Saunders. Each get $500,000 buyouts.
Pittsburgh left-hander Wandy Rodriguez exercised a $13 million player option. The 34-year-old went 6-4 with a 3.59 ERA, missing the final four months of the season with discomfort in his left forearm. His deal originally included a team option, but it became his when the Astros traded him in July 2012. Houston will pay $5.5 million of next year's salary.