The Lords gave final approval to the measure yesterday in an unopposed voice vote. Pro-equality peers wore pink carnation boutonnieres symbolizing their support for equal marriage.
The last remaining step is the Royal Assent, where the Queen, as Sovereign and Head of State, approves (assents to) a bill after it's passed by Parliament. This is merely a formality -- no monarch has withheld the Royal Assent since 1708; the equal marriage bill is expected to receive the Assent and become an Act of Parliament this week.
The measure applies to England and Wales; Scotland and Northern Ireland must move separately on the issue as they decide their own marriage laws.
Weddings are expected to begin in spring of next year.