Rachel Reeves and David Lammy are among a number of senior ministers set to leave government as the new prime minister prepares to appoint his new cabinet.
These ministers will make up the top team in his new government, helping to deliver the policy agenda that he sets out.
Ahead of the major reshuffle, business secretary Peter Kyle, and housing secretary Steve Reed, have both also resigned.
Mr Burnham has been tight-lipped on his choice of appointments in the run-up to his inauguration, with speculation reaching fever pitch over the weekend.
Allies of Ms Reeves have said that she was offered a “big job” in government but decided to decline it. In her resignation statement, she wished “the very best of luck” to her successor, Mr Burnham and his cabinet.
She wrote: “It has been the privilege of my life to serve as the Chancellor of the Exchequer.
“The economy today is stronger, fairer and more resilient because of the choices we have taken as a Labour Government over the past two years.”
Home secretary Shabana Mahmood is understood to be Mr Burnham’s favourite to be the next chancellor, in a move that some have warned could divide Labour MPs.
Meanwhile, the veteran politician’s long-time ally Ed Miliband is also tipped for a promotion from his current energy brief. Insiders have hinted that he may be bound for the role of foreign secretary after initially being linked to the Treasury job himself.
For the latest political updates on Andy Burnham’s first day as prime minister, follow The Independent’s live blog
An MP from 2001 to 2017, Mr Burnham has many allies in the halls of Westminster whom he may want to keep close as he forges a new path as prime minister.
The former mayor was a frontbencher during Gordon Brown’s administration – lasting from 2007 to 2010 – in a cabinet which at points also included current ministers Ed Miliband, Yvette Cooper, Pat McFadden and John Healey.
Delivering his inaugural speech on the steps of Number 10, Mr Burnham urged people to “pull me with me” to “build a new national sense of unity, of common purpose and positivity”.
“Let us make this the moment when Britain starts to believe again, the moment we bring back hope,” he said.
During his six-minute address, he said he would set out a ten-year plan for Britain later this year, and measure to tackle the cost of living on Tuesday to give people “breathing space now”.
He added: “I am acutely conscious that I am the sixth person in the last 10 years to walk up this street, the seventh prime minister since 2016, making this a moment for reflection and new resolution.
“It requires my generation of politicians to raise our game and rise to the new challenge.”
In the crowd for Mr Burnham’s speech was his long-term friend and ally, Liverpool mayor Steve Rotheram, former footballer Peter Reid, who played for Mr Burnham’s favourite team Everton, and Josh Simons, the former MP who stood in Makerfield to enable his return to Westminster.
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