Babbitt, who had taken a leave of absence Monday following news of the arrest, issued a statement late Tuesday.
"Serving as FAA administrator has been an absolute honor and the highlight of my professional career," Babbitt said in the statement. "But I am unwilling to let anything cast a shadow on the outstanding work done 24 hours a day, seven days a week by my colleagues at the FAA."
Transportation Department Secretary Ray LaHood thanked Babbitt for his years of service. FAA is housed within Transportation.
"Randy Babbitt has been a dedicated public servant and outstanding leader," LaHood stated. "On behalf of the American people, I thank him for his service and his leadership."
FAA Deputy Administrator Michael Huerta will act as FAA chief until a permanent replacement is found.
Babbitt was charged with drunk driving Saturday night by police in Fairfax, Va., The Washington Post reported. The Post said Babbitt, a former pilot who flew for 25 years for Eastern Airlines and was sworn in as FAA administrator in June 2009, faces a Feb. 2, 2012, court appearance. He was reportedly alone in his vehicle at 10:30 p.m. and was not involved in any accident. He was driving on the wrong side of Old Lee Highway, according to the arresting officer.
Babbitt also has served as president of the Air Line Pilots Association and as a member of FAA's Management Advisory Council. He came under scrutiny earlier this year after numerous reports surfaced of air traffic controllers falling asleep at their posts.
The commonwealth of Virginia has some of the toughest drunk driving laws in the country. Though Fairfax police don't release information on the blood-alcohol level of those charged, Babbitt will at the minimum face a $250 fine and a one-year revoked license.