The Columba Declaration commits the Churches to "grow together in communion and to strengthen their partnership in mission".
Founded in two different branches of Protestantism, England's Church is Anglican and Scotland's Presbyterian.
The two Churches will be debating the report over the coming months.
The Church of England's General Synod will hold a debate in February and the General Assembly of the Church of Scotland will consider the report in May.
The Columba Declaration appears within the Growth in Communion, Partnership in Mission report, which sets out the history of partnership between the two Churches and their shared beliefs.
The report states: "The new arrangements we are proposing are modest and 'light touch' with a small contact group meeting yearly and reporting to the ecumenical bodies within each Church."
The declaration has been authored by Kirk minister the Reverend John McPake, and the Church of England's Bishop of Chester, Peter Forster.
They say the agreement will allow clergy and lay people from each Church to be welcomed into the other when they move across the border.
The pact also recognises that the two Churches have constitutional responsibilities in separate parts of the UK.
Rev Alison McDonald, convener of the Church of Scotland's ecumenical relations committee, said: "The joint report sets out clearly the shared foundations of faith of the Church of England and the Church of Scotland, which enable us to recognise one another formally for the first time.
"This provides a sound basis for our ongoing co-operation and for exploring future partnership."
The Reverend Dr Jeremy Worthern, Church of England secretary for ecumenical relations and theology, said the Church valued its "ecumenical relationship with the Church of Scotland and our relationship within the Anglican Communion with the Scottish Episcopal Church".
He added: "There are opportunities for deepening both relationships as this report continues to be discussed and received by the Churches."
A report proposing an agreement between the Church of England and the Church of Scotland has been published, ahead of a debate by the Churches' ruling bodies.