The Prime Minister has invited Mark Drakeford to a UK summit bringing together political leaders to discuss the country's way forward in the weeks and months ahead.
Boris Johnson has written a letter to Mr Drakeford congratulating him on his re-election as First Minister and emphasising the "enormous potential of our United Kingdom".
The Prime Minister wrote: "You have rightly made COVID recovery a priority. To that end, I would like to invite you to join me, UK Government colleagues and others at a summit meeting to discuss our shared challenges and how we can work together in the coming months and years to overcome them.
"I will be writing in similar terms to the First Minister of Scotland, and the First and Deputy First Ministers of Northern Ireland.
"We will all have our perspectives and ideas - and we will not always agree - but I am confident that by learning from each other we will be able to build back better, in the interests of the people we serve."
Welsh Labour won the Senedd election on Saturday after it emerged they had secured 30 seats - just one short of an overall majority.
On Sunday Labour also performed well across the Police and Crime Commissioner elections in Wales, taking three of the four positions.
Plaid Cymru's Dafydd Llywelyn was re-elected as the Dyfed-Powys Police and Crime Commissioner.
Mr Drakeford visited Porthcawl on Saturday in the wake of his party's election win and said that the PM should use the election success for Labour in Wales and the SNP in Scotland to "reset relationships" with the devolved nations.
"I think now is the right moment to reset some relationships across the UK for a genuinely serious look at the way in which we can create machinery that allows all four parts of the United Kingdom to come together and create a successful future for us all", he said.
In his letter, the Prime Minister said he felt it was the United Kingdom - "Team UK" - that had helped Wales chart a course through the pandemic.
He wrote: "People across the UK, and in particular, the people of Wales are best served when we work together.
"Our vaccine roll-out has been a clear demonstration of that fact.
"The UK Government procured vaccines at scale for citizens across the UK.
"The dedicated and hardworking staff of the NHS in Wales excelled in getting jabs into arms from Cardiff to Caernarfon.
"This is Team UK in action, and I recommit the United Kingdom Government to working with the Welsh Government in this cooperative spirit."
The Welsh Conservatives will be the second biggest party in the Senedd, after they returned a record 16 MSs.
Party leader Andrew RT Davies said he felt it was a "good day's work at the office".
Plaid Cymru have 13 seats and the Liberal Democrats have one, with their leader Jane Dodds being elected into one of the Mid and West Wales regional list seats.
For more on the 2021 Senedd elections: