Rivera, with 608 saves in the regular season and 42 more in the postseason, is a 12-time All-Star. The Yankees say his recovery from June 12 knee surgery will be complete by opening day.
By then, Martin will be handling a new pitching staff in Pittsburgh after spending the past two seasons with New York.
The free-agent catcher goes from a franchise that's won a record 27 World Series titles to a team that has endured a record 20 consecutive losing seasons.
"It's going to be different," Martin said. "It's going to be a challenge but I think the Pirates have a young and electric club. There is a lot of talent there and I don't think we're as far away from winning as maybe people outside baseball think we are."
Humber, who threw a perfect game for the Chicago White Sox last season, was claimed off waivers by the Astros and agreed to a one-year contract. He gets an $800,000 salary next year and Houston holds a club option for $3 million in 2014 with a $50,000 buyout.
The 29-year-old right-hander went 5-5 with a 6.44 ERA in 26 games last season, including 16 starts.
Wilson was the 2010 major league saves leader with 48, but made only two appearances for the Giants this year after experiencing elbow trouble in April. He underwent ligament-replacement surgery April 19, his second such procedure on his pitching elbow after also having it done while in college at LSU in 2003, and missed the team's run to its second championship in three years.
The 30-year-old Wilson, who earned $8.5 million during his injury-shortened 2012 season, would be due to make at least $6.8 million next year under the rule limiting pay cuts to a maximum of 20 percent. By letting him go free, the Giants can sign him for a lower price, though the pitcher has apparently already hinted he will look for work elsewhere.
During the club's latest postseason run, Sergio Romo proved to be a reliable ninth-inning option in Wilson's place.
"I like our choices, including him being one, as we start the regular season," Giants general manager Brian Sabean said.
Jurrjens, an All-Star in 2011, was non-tendered by the Braves after getting demoted to the minors last season. Atlanta also declined to offer a 2013 contract to reliever Peter Moylan, but claimed right-hander David Carpenter off waivers from Boston.
The Red Sox cut ties with outfielder Ryan Sweeney and pitchers Scott Atchison and Rich Hill. Jack Hannahan was let go by Cleveland, clearing the way for youngster Lonnie Chisenhall to start at third base.
Baltimore chose not to offer a contract to Reynolds, the strikeout-prone slugger who hit 23 home runs last season after connecting for 37 the previous year.
Pelfrey, a 15-game winner in 2010, made only three starts this year before having season-ending Tommy John surgery on his pitching elbow. The Mets let him go Friday, along with outfielder Andres Torres and reliever Manny Acosta.
Washington cut ties with pitchers Tom Gorzelanny and John Lannan as well as catcher Jesus Flores.
Soto, once an All-Star catcher and the 2008 NL Rookie of the Year, was let go by Texas.
Other players not offered contracts included pitcher Manny Parra (Milwaukee), outfielder Nate Schierholtz (Philadelphia), pitcher Jeff Karstens (Pittsburgh), outfielder Ben Francisco (Tampa Bay), third baseman Ian Stewart (Cubs) and reliever Daniel Schlereth (Tigers).
In other moves, the Angels claimed outfielder Scott Cousins off waivers from Seattle, the Yankees claimed right-hander Jim Miller off waivers from Oakland, and Miami claimed first baseman-outfielder Joe Mahoney off waivers from Baltimore.
Arizona released right-hander Brad Bergesen, and the Yankees designated infielder Jayson Nix for assignment.
Players agreeing to one-year contracts that avoided arbitration included Pittsburgh pitcher Charlie Morton ($2 million), Kansas City second baseman Chris Getz ($1.05 million), Oakland first baseman Daric Barton ($1.1 million) and infielder Adam Rosales ($700,000), and Indians right-hander Blake Wood ($560,000).