Wright, 37, pitched in relief for Seattle last year, appearing in 60 games with a career-best 3.16 ERA. A one-time innings-eating starter, Wright has pitched in relief exclusively since 2008.
Wright, a first-round pick of the Rockies in 1993, will be pitching for his 10th organization.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.