Beltre had a team physical Tuesday night with a press conference scheduled for Wednesday. The Angels were also thought to be in the running for Beltre.
Beltre, 31, is coming off an All-Star season with the Red Sox, with whom he signed a one-year contract last offseason. He batted .321 with 28 home runs and 102 RBIs and led the American League with 49 doubles.
The move shuffles Michael Young from third base to designated hitter, replacing free agent Vladimir Guerrero.
The Rangers, coming off their first World Series appearance in 50 years, spent the early part of free agency trying to hold onto ace Cliff Lee, who signed with the Phillies. Texas then inked 2006 Cy Young winner Brandon Webb, who is coming off major shoulder surgery and hasn't pitched since Opening Day 2009.
Beltre's previous long-term deal came after he hit .334 with 48 homers and 121 RBIs for the Dodgers in 2004. The Mariners gave him a five-year, $64 million contract ... and he never hit better than .276 in five disappointing seasons in Seattle.