Transforming the UK into a federal system will help the country "heal our divided society" following the Brexit and Scottish independence referendums, Kezia Dugdale said.
The Scottish Labour leader set out her plan for a new Act of Union, with increased powers for Holyrood, Cardiff Bay, Stormont and the English regions.
The new powers should include some of the responsibilities which will return to the UK after Brexit, Ms Dugdale said.
She has written to Prime Minister Theresa May to call for a "people's constitutional convention" to decide on a "new political settlement" for the whole country.
But she said Labour could go ahead and establish a convention even without the support of the Government.
In a speech at the IPPR think tank in London, she said: "After more than 300 years, it is time for a new Act of Union to safeguard our family of nations for generations to come.
"This would mean a radical reshaping of our country along federal lines where every component part of the United Kingdom - Scotland, Wales, Northern Ireland and the English regions - take more responsibility for what happens in their own communities, but where we still maintain the protection of being part of a greater whole as the UK."
She said her new settlement would help Scotland address its future after Brexit.
"We are now faced with a Tory Government in Westminster which looks set to force hard Brexit on the whole of the UK and an SNP Government at Holyrood which wants to exploit the divisions to win independence," she said.
Ms Dugdale said her plan, which she will ask Scottish Labour Party members to back at their conference in February, would help address those concerns.
"I believe a new federal UK, with a strong Scotland able to carry forward a significant relationship with Europe, is what people across Scotland have voted for.
"It goes far to meet the dual mandates of the Scottish people and gives us the best protection for our jobs and our economy."
She added: "Our union must be saved. We must heal our divided society. It is only Labour that can do that."
Ms Dugdale was not holding talks with Labour leader Jeremy Corbyn even though her speech was taking place less than a mile away from the Houses of Parliament.
She said: "I spoke to Jeremy last week and talked him through the basic bones of the speech, the direction of travel we are going in."
Under her proposals, powers over fishing, agriculture and workers' rights currently exercised from Brussels should be given to Holyrood after Brexit.
"While Brexit has led us into a period of instability and chaos, it also provides us with an opportunity to confront problems in our society and make lasting changes that have been long overdue," she said
SNP MSP Linda Fabiani said: "If Labour are finally committed to more powers for the parliament then we look forward to their fulsome support as we make the case - as we always have - for a parliament with full powers.
"However, Labour have been promising a supercharged, powerhouse, federalism-max for years - and consistently failing to deliver it."
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