The bill must still pass the state Assembly and be signed by Gov. Deval Patrick, The Boston Globe reported.
The law bars couples from marrying in Massachusetts when their unions would not be legal in their home state. It was aimed at interracial couples who could not marry legally in many states at the time.
The Roman Catholic Church opposed the repeal, with Cardinal Sean O'Malley of Boston and other bishops appealing to the Legislature. But there were no protesters outside and no senators supported the law.
"People have become resigned to the fact that all the chaos that was predicted in 2004 -- the sky was going to fall, it would be catastrophic -- it never happened. And so it has become, as we expected it would, as
much a part of the reality of life in Massachusetts as anything else," said Sen. Dianne Wilkerson, a Democrat.
The state Supreme Court ruled in 2004 that banning gay marriage violated the state constitution. Attempts to amend the constitution have failed.
Notable deaths of 2014 [PHOTOS]