Schieffer will be Selig's representative in overseeing the National League franchise, which has been thrown into financial turmoil due to the divorce battle between owner Frank McCourt and wife Jamie McCourt, who served as chief executive officer of the club until 2009.
"We are very fortunate to have someone of Tom Schieffer's stature monitor the operations of the Los Angeles Dodgers on behalf of Major League Baseball," Selig said in a statement. "Tom is a distinguished public servant who has represented the nation with excellence and has demonstrated extraordinary leadership throughout his career."
Schieffer was president of the Rangers from 1991-99 under an ownership group headed by former U.S. President George W. Bush.
He also served as the U.S. ambassador to Australia and Japan during Bush's presidency.
Selig has told the Dodgers the league office must sign off on any expenditure of $5,000 or more, ESPN.com reported.