Schoeneweis went 0-3 with a blown save and a 5.40 ERA in September as the Mets collapsed down the stretch for the second straight year. New York, which had 29 blown saves in 72 chances last season, overhauled its bullpen at the winter meetings by signing free-agent closer Francisco Rodriguez and acquiring J.J. Putz from Seattle.
Schoeneweis was 2-6 with a 3.34 ERA in 73 games -- including 1-4 with a 4.66 ERA after the All-Star break.
"We feel that Scott will help balance our bullpen," Arizona general manager Josh Byrnes said in a statement. "Given his success against left-handed hitters over the last several seasons, he provides us another weapon late in games."
The 35-year-old Schoeneweis limited lefty batters to a .178 average (18-for-101) last season.
New York agreed to pay $1.6 million of Schoeneweis' $3.6 million salary for 2009 and acquired right-hander Connor Robertson from the Diamondbacks. Robertson, who came over to Arizona in the Dan Haren deal, was 0-1 with a 5.14 ERA in six games this year.
Schoeneweis was implicated in a 2007 ESPN.com report that said he received six shipments of steroids in 2003 and 2004. Schoeneweis declined comment at the time of the report and the commissioner's office said there was insufficient evidence to penalize him for any violation of the sport's drug agreement with the players' association.
Schoeneweis, a survivor of testicular cancer, is 45-55 with a 4.91 ERA and nine saves in 10 major league seasons.
Also Friday, the Mets decided not to offer 2009 contracts to right-hander Ambiorix Burgos and infielder Argenis Reyes. Both became free agents.
Burgos, who spent last season on the disabled list following elbow ligament replacement surgery, is awaiting trial for a hit-and-run accident that killed two women in the Dominican Republic. He is accused of abandoning the victims and fleeing, charges that can carry six months to two years in prison.
Arizona didn't offer 2009 contracts to infielder Chris Burke, outfielder Jeff Salazar, catcher Robby Hammock and left-hander Wilfredo Ledezma. Salazar hit .211 in a career-best 90 games this year.