From Washington Post:
Washington Post reporter Tim Craig relays that the D.C. Council has voted 13-0, without debate, to recognize same-sex marriages performed in other states. Watch D.C. Wire for updates.
The approved law was added as an amendment to another bill, and can be seen on the second page of that bill's text (.pdf).
If Congress does not intervene, council member David A. Catania (I-At Large) has said that he will introduce a separate bill this year to allow same-sex marriages to be performed in the District.
After further debate, a second vote was taken, with D.C. Council member Marion Barry (D-Ward 8) deciding to vote against the proposal. The final count is 12-1 in favor of recognizing same-sex marriages performed in other states.
Images from DCforMarriage.com.