The decision follows some concern voiced by Anglo-Catholics that the priests of the Lutheran church in Denmark had lost the Apostolic succession - an unbroken line of layings-on of hands traceable back to Jesus' apostles, which is necessary to make a priest in Catholic theology.
The General Synod approved by an overwhelming majority the Porvoo Declaration, an ecumenical document committing the churches involved to full visible unity.
The chief practical effect of yesterday's vote will be that Scandinavian priests will be recognised in England, and that Scandinavian Lutheran bishops will be invited to the next Lambeth Conference.
It does not bind the wider Anglican Communion, or Lutheran churches outside Scandinavia and the Baltic States, though it is expected to be gradually extended in North America, according to Bishop Andreas Aarflot, the Lutheran Bishop of Oslo, who is at the synod.
The Bishop of Ely, the Rt Rev Stephen Sykes, argued that the Danes had not meant to break the apostolic succession in 1536 when the disputed ordinations took place.
However, the Rev John Broadhurst, chairman of Forward in Faith, a coalition group opposed to women priests, said that he was afraid that the agreement might produce a bloc of Northern European Protestant state churches, which would weaken the Church of England's historic commitment to an ordained priesthood.
"I fear that it will set a precedent for English non-conformist relationships. There are a lot of people talking as if episcopal ordination no longer matters," he said. Anglo-Catholics have successfully blocked earlier schemes for reunion with the methodists on the grounds that they had not been properly ordained by bishops, but defeat on the ordination of women has weakened their position.Reuse content