Financial terms of the deal were not announced but sources have told ESPNNewYork.com's Adam Rubin that Francisco's deal is worth $12 million.
The 32-year-old Francisco went 1-4 with 17 saves and a 3.55 ERA in 54 games with the Toronto Blue Jays in 2011. The right-hander has appeared in 50 or more games in each of the last five years. He had 25 saves with the Rangers in 2009.
Francisco is 18-19 with a 3.72 ERA with 368 strikeouts in 334 innings in seven years with Texas and Toronto.
The deal was announced Monday.
Information from The Associated Press was used in this report.