Major League Baseball announced Texas had won the star right-hander's posting rights that were reportedly in excess of US$50 million.
The Rangers reportedly out-bid teams that included the Toronto Blue Jays, New York Yankees and Chicago Cubs for the right to speak with Darvish.
The negotiating fee goes to Darvish's Pacific League team, the Hokkaido Nippon Ham Fighters, as a transfer fee if the pitcher agrees to a deal with Texas.
The Rangers now have 30 days to sign Darvish. The 25-year-old has a career record of 93-38 with a 1.99 earned-run average.