A new cabinet post and fund should be set up as part of plans to strengthen the union, a review has said.
The Dunlop Review was set up in 2019 by then-Prime Minister Theresa May, to ensure UK government departments worked in the best interests of devolution.
Cabinet Office Minister Michael Gove said the report had provided "constructive" reforms.
But SNP MP Ronnie Cowan dismissed it as "Tory tinkering" and said the report's recommendations were "outdated".
Mrs May announced the review during her final visit to Scotland as prime minister.
The report was completed in November 2019, but was published on Wednesday.
In the report, Lord Dunlop said establishing a new cabinet position for "intergovernmental and constitutional affairs" would give union issues "greater visibility".
He also said the minister in the role would have "a duty to uphold the integrity of the constitution".
The review recommended that spending by the UK government in Scotland, Wales and Northern Ireland should be clearly marked with UK government branding.
And it said a fund for UK-wide projects "to incentivise" schemes that strengthen the union should be established.
A second portion of the fund would be open to bids from UK government departments and devolved governments working in co-operation.
Lord Dunlop said this would "encourage collaborative working and policy innovation in different parts of the UK".
He said the UK's intergovernmental relations were "not fit for purpose" and advised the government to set up a "UK Intergovernmental Council" to ensure the UK consulted devolved governments.
"Taken as a whole these proposals are intended to build trust and respect between the institutions of government in the UK," Lord Dunlop wrote.
'The ties that bind us'
Responding to the report, Cabinet Office Minister Michael Gove said the UK government shared the review's ambition to "strengthen the ties that bind us across the whole United Kingdom".
He said the government had, in order to strengthen the union, set up new structures to "maintain regular, meaningful and effective cooperation" between the UK government and the devolved administrations.
He also said the civil service training programme now included sections on devolved issues.
And he added that the government planned to move 22,000 roles out of London and the South East by 2030, with some jobs going to Scotland, Wales and Northern Ireland.
While Mr Gove didn't address the call for a new cabinet minister directly, he said all secretaries of state - senior government ministers - had "a critical role in representing the distinctive voices and interests of Scotland, Wales and Northern Ireland in Whitehall and in Cabinet".
However, the SNP's Mr Cowan said: "This long-delayed review confirms only one thing - that Scotland doesn't need Tory tinkering with the constitution, we need independence."
He described the recommendations in the report as "outdated" and "half-measured".
DUP MP Sir Jeffrey Donaldson said: "The publication of the Dunlop Report and the response from the government, are positive steps in terms of promoting the union and on binding the UK together, but the major fly in the ointment remains the Northern Ireland Protocol, which this government created and implemented.
"It is deeply damaging to the union as it places a trade border between us and the rest of the United Kingdom."
Member of the Senedd and Wales' Counsel General, Jeremy Miles, said it was "disappointing that after three years of discussion, we still have no overall agreement."
He added that in the same three year period "the tone of inter-governmental relations has deteriorated due largely to a series of aggressive intrusions by the UK Government into areas of devolved competence."