As it stands, the Methodist Church has become the largest religious denomination in Britain to permit same-sex marriages.
A vote to change the definition of marriage at the Methodist Conference on Wednesday overwhelmingly passed by 254 in favour with 46 against.
Freedom of conscience clauses mean ministers will not be forced to conduct such weddings if they oppose the move.
Same-sex marriage is not allowed in the Church of England or the Roman Catholic Church. However, it is welcomed in the Scottish Episcopal Church, the United Reformed Church and the Quakers in Britain.
The Methodist Church is Britain’s fourth largest Christian denomination with about 164,000 members across more than 4,000 churches.
Church officials hope the first same-sex weddings in Methodist chapels will take place in the autumn.
The Rev Sam McBratney, chair of the Dignity and Worth campaign group, said it was a “momentous step on the road to justice” after many years of “painful conversations”.
“Some of us have been praying for this day to come for decades, and can hardly believe it is now here,” he said. “We are so grateful to our fellow Methodists for taking this courageous step to recognise and affirm the value and worth of LGBTQ+ relationships.
“We reassure those who do not support this move that we want to continue to work and worship with you in the Church we all love.”
However, in an emotional debate, Carolyn Lawrence, a former vice-president of the Methodist Conference, warned there was a “significant minority” of Methodists who were “planning on leaving or resigning their membership” as a result of the vote.