The 35-year-old is the newest member of an overhauled bullpen in Texas, signing a one-year contract worth $1.5 million US.
Frasor has spent all but 20 games of his nine-year major league career with Toronto.
"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 locked up one of the two wild-card spots in the American League in 2012, tying Baltimore with a record of 93-69.
Frasor, the Jays’ all-time leader in career pitching appearances (505), was dealt to the Chicago White Sox midway through the 2011 season.
He is coming off a 2012 campaign during which he missed seven weeks with an inflamed right forearm.
Frasor returned for the final month of the season after the only disabled list stint in his career. The right-hander 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."
He posted a 4.12 earned-run average in 50 games, striking out 53 and walking 22 over 43 2/3 innings.
In his career, Frasor sports a 26-31 record, 3.77 ERA and 36 saves in 525 innings pitched.
So far this off-season, Texas has lost free-agent relievers Koji Uehara (Boston), Scott Feldman (Chicago Cubs) and Mike Adams (Philadelphia) while reliever Alexi Ogando has been moved to the starting rotation.