A former Goldman Sachs banker, Mr Sunak has been appointed as the second most powerful minister in the British government as Prime Minister Johnson reshuffled his cabinet and Pakistani-origin Sajid Javid unexpectedly resigned.
He added: "It's been a huge privilege to shape the new Future Of Transport Strategy at @transportgovuk @grantshapps & brilliant DFT team, & help the PM make this an inspiring @OneNationCons government of renewal".
In the wake of Brexit, Johnson has vowed to take a more interventionist economic approach than some of his Conservative predecessors in order t o boost poorer regions outside the economic hub of London and southeast England.
Julian Smith was also sacked as Northern Ireland Secretary - weeks after he brokered the deal that restored the power-sharing administration in Stormont.
Newcomers at the cabinet meeting on Friday will include Anne-Marie Trevelyan, who replaces Alok Sharma as worldwide development secretary; Amanda Milling, who is minister without portfolio and chairwoman of the Conservative Party; and Suella Braverman, who takes on the role of attorney general after the prime minister asked Mr Cox to step down.
Javid chose to quit instead, and was replaced by his former deputy at the Treasury, Rishi Sunak, in the biggest shock of Johnson's shake-up of his ministerial team.
The bombshell - less than a month before the Budget - follows tensions between Mr Javid and Mr Johnson's senior adviser Dominic Cummings.
Mr Jenrick, a former Treasury minister, told BBC Breakfast: "What was proposed and is now going to happen is that we bring together the back office teams that advise the Prime Minister at Number 10 and those that advise the Chancellor".
Chief Whip Mark Spencer, also quizzed on his way into Number 10, was asked if Mr Javid had been forced out of the Cabinet.
Britain's Press Association news agency reported that Javid had quit after being told to fire all his aides and replace them with staff appointed by the prime minister's office. He has less than a month to deliver his first budget on March 11.
Mr Javid accused the PM of setting conditions "any self-respecting minister" would reject - seen as a thinly veiled swipe at his successor.
Along with the ministerial exits, the reshuffle - which Downing Street insiders had predicted would be "conventional" before the row with Javid - included promotions for MPs who are highly rated by Number 10.
Alok Sharma was promoted from worldwide development to become the new business secretary and he will also be minister for the Cop26 United Nations climate summit.
George Eustice was promoted to environment secretary from his previous role in the same department.
Ex-Brexit secretary Stephen Barclay has replaced Sunak as treasury chief secretary.
- Esther McVey lost her job as housing minister.
Most of the key players, including Home Secretary Priti Patel, Foreign Secretary Dominic Raab and Chancellor of the Duchy of Lancaster Michael Gove, retained their positions.