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.
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. 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 60 home runs the past two years.
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.
The AL champion Tigers did not offer a contract to reliever Daniel Schlereth.
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 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).
Pittsburgh made a pair of small trades, acquiring minor league right-hander Zach Thornton from Oakland for reliever Chris Resop, and minor league pitcher Jhondaniel Medina from Baltimore for infielder Yamaico Navarro.
Elsewhere, former big leaguer Chan Ho Park announced his retirement. The first South Korean-born player in the majors and a 2001 All-Star, he holds the major league record for wins by an Asian pitcher (124).
AP Sports Writer Ronald Blum contributed to this report.