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."

Celtic and Dundee are exploring the possibility of staging a game in the US, where the Kilmarnock striker has experience with Portland Timbers.
"I think there are avenues for the Scottish game to tap into if you look at the American model," said Boyd.
"But, for our teams to go there to play, I don't think it's right."
A formal proposal is set to be put before the Scottish Professional Football League regarding the Dundee v Celtic match in the next few weeks, with Boston and Philadelphia possible host cities.
"It's not for me," Boyd, 32, told BBC Scotland. "With the two of them being Scottish clubs, it's right that they play in Scotland.
"It's obviously a big market for Celtic with them being a worldwide club and because Dundee's owners are American, that's why they'll be trying to explore it.
"There's a lot of Scottish people living in America. There is interest.
"But the majority of Dundee fans will be from Dundee. I don't imagine there'll be a lot in America. With Celtic, there will be. That comes with the size of the club."
Boyd spent 2012 in Major League Soccer, scoring seven goals in 22 starts for Portland.
"Scottish clubs can go over and see what's going on and try and make things better but bring it back here to try and make the Scottish game better in Scotland," added the former Scotland international.
"Football is definitely getting bigger [in the US].
"The majority of clubs are now playing in front of 20,000 every week. Seattle are playing in front of 60,000 - that's as big as Rangers and Celtic!
"There's more to take into it - the travelling, the different climates, the time zones. It's a difficult place to go and play football.
"And they change the rules every year as well to suit the teams that are struggling because if you win the league then players' wages might go up then the next thing they need is to trade their players to keep themselves under their salary cap.
"It would be difficult to manage in and definitely be an owner in but the flipside is that if you're an owner and you're getting 20,000 every week, you know you're still making money."
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.
[NEXT_CONCEPT]
Kris Boyd believes Scottish football can learn from the United States but is against the idea of playing Scottish Premiership matches overseas.