Same-sex marriages would be recognized nationwide under a bill passed by the Senate. There were 12 Republicans who voted for the legislation.
The bill is going to the House, which is expected to pass it next week, and then to the president's desk.
Schumer wore a tie to his daughter's wedding and celebrated the passage of the bill.
Schumer said that Tuesday was a good day for millions of Americans.
The "Respect for Marriage Act" was passed by the House in July in order to protect marriage equality.
When the legislation passed the House, a total of 47 Republicans voted for it, but the effort was put on hold in the Senate due to religious liberty concerns. The bipartisan group of senators led by Baldwin and Collins negotiated the version of the bill that passed Tuesday.
Biden said in a statement on Tuesday that he would "proudly" sign the bill into law once the House passes it.
He said that love is love and that Americans should have the right to marry the person they love.
The 1996 Defense of Marriage Act was deemed unconstitutional by the Supreme Court and would be repealed.
A large majority of Americans support same-sex marriage rights. A majority of Americans support marriage equality.