Short decided make the move to Arlington. On September 21, 1971, by a vote of 10 to 2 (the Orioles’ Jerold Hoffberger and John Allyn of the Chicago White Sox registered the dissenting votes), American League owners granted approval to move the franchise to Arlington, Texas for the 1972 season.

Senators fans were livid. Enmity came to a head at the club’s last game in Washington. Thousands of fans simply walked in without paying after the security guards left early, swelling the paid attendance of 14,460 to around 25,000, while fans unfurled a banner reading “SHORT STINKS”. With the Senators leading 7–5 and two outs in the top of the ninth inning, several hundred youths stormed the field, raiding it for souvenirs. One man grabbed first base and ran off with it. With no security in sight and only three bases, umpire crew chief Jim Honochick forfeited the game to the New York Yankees.

In April 1989, Rangers owner and oil tycoon Eddie Chiles, sold the team to an investment group headed by George W. Bush, son of the President of the United States, George H. W. Bush. After hearing that Chiles planned to sell the team, Bush headed a group of investors that bought the team for $89 million. While his own equity in the team was a small one (approximately 1%), he was named Managing General Partner of the new ownership group. He increased his investment the following year.

During his tenure, the Rangers and the City of Arlington decided to replace the aging Arlington Stadium with a new publicly funded stadium, at a cost of $193 million, financed by Arlington residents, through a sales tax increase. Ground was broken on October 30, 1991 on what would become The Ballpark in Arlington (now named Rangers Ballpark in Arlington). The city, through the Arlington Sports Facilities Development Authority, also controversially authorized the seizure of 13 acres (53,000 m2) of land through eminent domain for the Rangers future development. Landowners filed lawsuits over the acquisition and eventually won settlements of $22.2 million which the Rangers failed to pay. On March 19, 2007, the Texas Rangers severed their relationship with Ameriquest and announced that the stadium would be named Rangers Ballpark in Arlington. On February 5, 2014, Globe Life and Accident Insurance Company bought the naming rights to the stadium. Globe Life is owned by Torchmark Corporation, which is based in McKinney, Texas, a northern suburb of Dallas.

The stadium contains 5,704 club seats and 126 luxury suites.