Rangers General Manager John Hart, who helped build the Indians' dynasty during the 1990s, also acquired righthander Ryan Drese for a pair of 25-year-olds -- righthander Aaron Myette and first base prospect Travis Hafner.
One of the best catchers in history, Rodriguez will become a free agent Saturday at midnight if the Rangers do not offer him salary arbitration.
While it was believed they would cut payroll by not re-signing Rodriguez, a 10-time All-Star and former MVP who collected $9.6 million last season, that now appears to be a certainty.
Diaz was Cleveland's No. 1 catcher most of the last four seasons, playing a career-high 134 games in 2001.
The 29-year-old Diaz is a lifetime .259 hitter with 15 home runs and 139 RBI in 456 games, all with the Indians, and has thrown out 32.8 percent of potential base stealers. He is signed through 2004 with a club option for 2005.
Rodriguez is one of only two catchers in history to win 10 consecutive Gold Gloves, doing so from 1992-2001, his first 10 full seasons in the major leagues. Anaheim's Bengie Molina snapped his string this year.
A 31-year-old from Puerto Rico, Rodriguez has been plagued by injuries in recent years. He missed 176 games from 2000-02 with a broken thumb and troubling back ailment.
When healthy, Rodriguez has been the best catcher in baseball. He was named American League MVP in 2000, when he hit .332 with 35 home runs and 113 RBI, and is a .305 batter lifetime.
The Rangers parted with a good prospect in Hafner, who hit .342 with 21 home runs and 77 RBI in 110 games last year at Class AAA Oklahoma. The 25-year-old led the Class A South Atlantic League in home runs and RBI in 1999 and hit .346 at Class A Charlotte in 2000.
Despite being given every opportunity on a porous pitching staff, Myette, 25, failed to impress. He went 2-5 with a 10.06 ERA in 15 games last season. In 48 1 /3 innings, he allowed 64 hits while walking 41 and striking out 48.
Drese, 26, was not much better for Cleveland during his rookie season of 2002, going 10-9 with a 6.55 ERA in 26 starts. He is 11-11 with a 5.90 ERA in 35 major league appearances.
The Rangers also agreed to terms with free agent righthander Rudy Seanez, who was 1-3 with a 5.73 ERA in 33 games for Texas last season.
Texas also must offer arbitration or reach a contract agreement with lefthander Kenny Rogers and outfielder Todd Hollandsworth or risk losing negotiating rights with them intil May 1.