Commissioner Bud Selig made the appointment Monday, less than a week after Major League Baseball took over operation of the franchise from owner Frank McCourt.
Schieffer was the club president from 1991 to 1999 and the Rangers' general partner from November 1994 until June 1998.
"Tom is a distinguished public servant who has represented the nation with excellence and has demonstrated extraordinary leadership throughout his career," Selig said in a statement.
Selig also said that Schieffer's longtime experience in managing the Rangers will benefit the Dodgers franchise.
Schieffer was the club's partner in charge of ballpark development before the 1994 opening of the Rangers' new stadium. The Rangers won their first three AL West titles in 1996 and 1998-99 during Schieffer's tenure.
As the president of the Rangers, Schieffer was a member of several MLB committees and boards, including the 1999 Blue Ribbon Task Force on Baseball Economics.
The 63-year-old Fort Worth native also served three terms as a Democrat in the Texas House of Representatives after being elected at the age of 25.
Schieffer also served as the U.S. ambassador to Australia from 2001-05 and then as the ambassador to Japan from 2005-09 under President George W. Bush.
The Dodgers have been in near constant turmoil since October 2009, when Jamie McCourt filed for divorce a week after husband Frank fired her as the team's chief executive.
The Associated Press contributed to this report.