Connolly, a Republican, was appointed by President George W. Bush.
His resignation was expected because of Democrat Barack Obama's election as President and the Obama administration's new appointments and Senate confirmation.
Connolly took office as U.S. Attorney for Delaware Sept. 4, 2001. Connolly has said he will go into private practice.
President Bush Nominated Connolly to become a federal judge but that nomination stalled in the Senate and Connolly never got a hearing.