The Rangers have not confirmed the deal, which was first reported by CBS Sports writer and MLB Network insider Jon Heyman. Choo will need to pass a physical exam before the contract is finalized.
By landing the biggest free-agent position player still on the board, Texas is now likely out of any running to land Japanese pitcher Masahiro Tanaka, should he be posted. But the Rangers are putting their resources into adding production to an offense that slipped to seventh in the American League in runs and on-base percentage last season.
Choo, 31, had the fourth-highest on-base percentage in the Majors in 2013 for the Reds at .423, trailing only Miguel Cabrera, Joey Votto and Mike Trout.
Choo hit .285 with 21 home runs, 54 RBIs, 107 runs scored and 20 stolen bases in his season with the Reds after playing the previous seven years for the Indians. He originally was signed by the Mariners in 2000 as an international free agent out of South Korea.
Choo was traded by Seattle to Cleveland in 2006 just as he was beginning his Major League career, then was sent to the Reds prior to last season.
The left-handed-hitting Choo has a career line of .288/.389/.465 with an .854 OPS, and he has averaged 19 stolen bases per year over the past five seasons.
Choo's addition means the Rangers have now moved on from free-agent outfielder Nelson Cruz and will likely go with the trio of Choo in left, Leonys Martin in center and Alex Rios in right.
The infield also will have a new look, with Fielder at first and young Jurickson Profar taking over for Kinsler at second, alongside returnees Elvis Andrus at shortstop and Adrian Beltre at third.
The Rangers went 91-71 last year, but missed the playoffs for the first time since 2009. They were in the top four in on-base percentage in the American League from 2010-12, but fell to seventh last year at .323. Choo's .423 on-base percentage was the fifth highest by a left-handed-hitting outfielder in the Majors over the past 10 years.
Choo's career-high OBP was boosted by a Major League-leading 26 hit-by-pitches and 112 walks, which eclipsed his own previous high of 83 in 2010.
This is the first shot at free agency for Choo, who is represented by Scott Boras. Choo earned $7.35 million last season in his final season of arbitration eligibility.