The first nuptials took place just after midnight in England, making it the first place in the UK to allow such ceremonies. Scotland has also passed a law agreeing same-sex marriage.
A letter signed by the Bishop of Buckingham, the Rt Rev Alan Wilson, several retired Church of England bishops and five Anglican cathedral deans, said marital law had evolved "over the centuries in response to changes in society".
They said: "We rejoice that same-sex couples will be able to marry in England and Wales.
"As persons of faith, we welcome this further development in our marriage law, which has evolved over the centuries in response to changes in society and in scientific knowledge.
"We acknowledge that some - though not all - of the faith organisations to which we belong do not share our joy, and continue to express opposition in principle to such marriages."
However, they added that the time would come when people of all faiths would accept it.
The emblem of lesbian, gay, bisexual and trans-gender groups, the Rainbow flag, was flown over the Scotland Office and Cabinet Office yesterday.
Deputy Prime Minister Nick Clegg told the Liberal Democrats Scottish conf-erence today marks a "special day" and the UK a different place, for the better.