The deal, which was not officially announced by the Rangers, is worth a reported $130 million, CBSSports.com said.
Choo was one of the most sought-after free agents of the hot stove season after he enjoyed a productive season as leadoff man for the Cincinnati Reds. Choo, 31, hit .258 with 21 home runs and 54 RBI.
In nine Major League season, Choo has compiled a .288 average with Seattle, Cleveland and the Reds.
MLB.com said the signing, which is contingent on Choo passing a physical, should provide some new blood for the Texas offense, which slipped to seventh in the American League in runs scored last season.
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