The 35-year-old right-hander spent most of his career with Toronto, setting a Blue Jays franchise record with 505 appearances since his major league debut in 2004.
Frasor was 1-1 with a 4.12 ERA in 50 games last season, when he was on the disabled list more than six weeks because of right forearm tightness. He returned for the final month of the season after the only DL stint in his career. Frasor said he feels good, which he said was confirmed by the extensive physical he underwent Wednesday including X-rays and an MRI.
"Picture after picture," Frasor said. "The doctor afterward, he said everything went great. That goes along with how I feel, really, really good."
Frasor was traded from Toronto to the Chicago White Sox midway through the 2011 season, but was dealt back to the Blue Jays at end of that year. He is 26-31 with 26 saves and 3.77 ERA in 525 career games, including 20 with the White Sox.
"When it became clear the door in Toronto has closed ... I just wanted to go to a winner," Frasor said. "I didn't sniff a playoff race. I wanted to be on a great team. I'm thrilled. This is a perfect opportunity."
Texas designated catcher Eli Whiteside for assignment to make room on its 40-man roster.
Notes: The Rangers will play their season opener at new AL West rival Houston on Sunday night, March 31, for a national ESPN broadcast. After an off day Monday, the rest of that season-opening series will be played Tuesday and Wednesday (April 2-3). ... The Rangers announced their minor league coaching staffs Thursday. That includes the return of minor league managers Bobby Jones at Triple-A Round Rock and Steve Buechele at Double-A Frisco.