The UK government says it will consult the devolved administrations on a key part of Brexit legislation.
Brexit Secretary David Davis confirmed the administrations would be asked to consent to the Repeal Bill, which aims to turn EU laws into UK laws so they can then be changed if required.
He urged the devolved nations to "come together" and support the legislation.
The move, which was welcomed by the Scottish and Welsh governments, does not mean they can block Brexit.
The Repeal Bill is central to the UK's withdrawal from the EU. As well as ending the jurisdiction of the European Court of Justice, it will also bring EU law onto the UK statute book so Parliament can decide which parts to retain.
Under a political convention between the devolved institutions and Westminster, any new law that relates to devolved matters needs a legislative consent motion passed.
The Repeal Bill does cover devolved areas, particularly in farming and fisheries.
However the convention does not have legal force, so it will not allow any of the administrations to veto the legislation.
Ministers had previously suggested consent would be required for the new legislation.
Confirming the position during a Commons debate about Brexit, Mr Davis said: "We expect there will be a significant increase in the decision-making power of each devolved administration once we exit the EU.
"That's why, given that this bill affects the powers of devolved institutions and legislates in devolved areas, we will seek the consent of the devolved legislatures of the bill.
"We would like everyone to come together in support of the legislation, which is crucial to delivering the outcome of the referendum."
A Welsh Government spokesman said: "We hope this means they have been listening and taking seriously our very strongly felt concerns that this legislation must not in any way restrict the powers and competencies of the Assembly.
"As set out in our policy paper, Brexit and Devolution, leaving the EU must be about the future, not the past.
"We must work with England, Scotland and Northern Ireland - through discussion, not diktat - to map our collective future."
Plaid Cymru's Brexit spokesman, Hywel Williams also welcomed the news.
Mr Williams said: "The UK government must now publish full details on how the governments of each different UK country will be involved in the process of drawing up the Great Repeal Bill."
Stephen Gethins, the SNP's international affairs spokesman, said his party would always protect Scotland's interests, and called for full details to be published on how the devolved administrations would be involved in Brexit negotiations.