Chavez, 32, played 54 games with Seattle last season before suffering a torn anterior cruciate ligament in his right knee in June. He batted .273 with two home runs, 13 RBIs and 17 runs scored for the Mariners last season, making 44 starts in the outfield.
The native of Venezuela had surgery to repair the ACL tear in July and is not expected to be fully recovered for the start of the season.
Chavez' major league career, which began in 2001, includes stays with Kansas City, Montreal, Washington, Philadelphia, the New York Mets and Seattle. He played in 10 postseason games for the Mets in 2006, including all seven in the Mets' series loss to St. Louis in the National League Championship Series.
Monday's deal gives the Rangers 15 non-roster players for spring training.
If Chavez is added to the 40-man roster, he would get a $1 million, one-year contract, and the Rangers would have a $1.25 million option for 2011 with a $50,000 buyout. If he has at least 30 days on the active roster during the 2010 season, the buyout would increase to $100,000.
He can earn an additional $180,000 in performance bonuses and $300,000 in roster bonuses this year, getting the full amounts for 250 plate appearances and 160 days on the active roster. The option year includes $750,000 in performance bonuses based on plate appearances up to 575.
Information from The Associated Press contributed to this report.