As expected, starter Cliff Lee turned down his arbitration offer to become a free agent. The Rangers would get a first-round draft pick and a supplemental pick in the 2011 draft if Lee signs with another club.
The Rangers and Francisco still have to work out the details of a new contract.
Francisco, 31, was 6-4 with a 3.76 ERA in 56 games for Texas in 2010. He missed all of September and the playoffs with a strained muscle in his right side but is expected to be ready for spring training.
Francisco started the season as the closer but was moved to eighth-inning setup after struggling in the ninth inning of several games the first week of the season.
Neftali Feliz took over as the closer and ended up with 40 saves and the AL Rookie of the Year Award.
But the change in roles didn't diminish Francisco's importance to the bullpen. The hard-throwing right-hander was the primary eight-inning setup man and did the job.
His value was evident when the club struggled to fill the void his absence created down the stretch and in the playoffs after he went on the disabled list Aug. 28 and didn't return. Manager Ron Washington had to try to piece together the late innings based on matchups instead of simply handing the ball to Francisco for three outs in the eighth.
Francisco also gives the Rangers another arm with closer experience to end games when Feliz is not available. Francisco had 25 saves in 2009.