Members backed a motion welcoming a joint report published last year, which sets out proposals on how clergy from each church could become eligible to serve in the other.
The report, Mission and Ministry in Covenant, which was co-written by the two churches' faith and order bodies, also sets out how the Methodist Church could come to have bishops in the historic episcopate.
The motion acknowledges that there is further work to do to clarify a number of areas, including how the proposals would be worked out in practice.
It also calls on the Church of England’s Faith and Order Commission to update Synod at its next group of sessions in July of this year on this work.
But an amendment to the motion speaks of “confident hope” that outstanding issues can be resolved quickly.
Speaking during the debate the Archbishop of Canterbury, Justin Welby, said: “I want to support this motion very strongly indeed.
“It seems to me that in voting for it we respond to the word of God in the scriptures where there is a clear command to unity in diversity and in responding to this paper positively we respond to the Spirit who is already working in both of our Churches bringing us together.”
Opening the debate, the Bishop of Coventry, The Rt Revd Christopher Cocksworth, Chair of the Church of England's Faith and Order Commission, said the proposals would be a step towards “healing a tragic division in the Church of England” when the two churches separated almost 200 years ago.
He said: “These proposals concern reconciliation between churches.
“The reception of the historic episcopate by the Methodist Church and the Church of England’s declaration – no, celebration, eucharistic celebration – of being ‘in communion’ with the Methodist Church, [would] re-order our relationship and takes us a vital step towards full visible unity.”
The Archbishop of York, Dr John Sentamu, told Synod: “I believe that the time has come for our two church traditions (Methodism and Anglicanism) to consult the people of God – the Laos, the Laity.
“A mute button must be switched off for the sake of the Kingdom of God and the urgent need to re-connect our two Church traditions with England. All has to do with God’s Mission.”
The report builds on the theological convergence established by 'An Anglican-Methodist Covenant', signed in 2003, and the subsequent work of the Covenant's Joint Implementation Commission.
In 2014 the General Synod of the Church of England and the Methodist Conference mandated the faith and order bodies to bring forward proposals that would enable the interchangeability of ordained ministries in the two churches.
Notes to editors:
Overall the voting was as follows:
Bishops: 35 for with two against and no abstentions
Clergy: 131 for, with 23 against and 13 abstentions
Laity: 124 for, with 34 against and 11 abstentions
For a full list of churches with which the Church of England is currently in communion, please see Part 4 of the Church of England Year Book.