Badger was born on April 17, 1795 in New Bern, North Carolina. Following a partial college education at Yale University, he studied law and was admitted to the bar in 1814. Badger practiced law in North Carolina, was active in state politics and held public office on occasion. A supporter of Andrew Jackson from the 1820s, he separated with him in the mid-1830s, became a leader of the Whig party and helped carry the Whigs to victory in the 1840 Presidential election.

Upon taking office, President William Henry Harrison appointed Badger as his Secretary of the Navy, and he continued in that post when John Tyler succeeded to the Presidency upon Harrison's death. Badger's brief term as Secretary was marked by efforts to strengthen the Navy in the face of tension with Great Britain, the establishment of the Home Squadron and continued interest in steamships.

Badger resigned in September 1841, during a general cabinet shakeup. He was elected to the Senate in 1846 and remained a Senator until 1855. He was nominated by President Millard Fillmore as an Associate Justice of the Supreme Court in 1853, but was not confirmed by the Senate. He was a Unionist during the secession crisis but thereafter supported the Confederate war effort. Badger died in Raleigh, North Carolina on May 11, 1866.

Two Navy ships have been named in honor of Senator Badger: USS George E. Badger (DD-196), and USS Badger (FF-1071). A Liberty ship, the SS George E. Badger, also was named in his honor.