Zahawi said his focus is “very much” rebuilding the economy after the pandemic, as well as battling against inflation.
On BBC Breakfast, the new chancellor said: “Inflation is – if allowed to get out of control – deeply damaging.”
Zahawi grew up in Britain after his parents were forced to flee Iraq.
He went on to launch polling company YouGov and, according to the BBC, is believed to be one of the richest politicians in House of Commons.
The MP for Stratford-Upon-Avon became education minister in September 2021 following a cabinet reshuffle.
Sunak said that stepping down while the world is battling against economic consequences of the pandemic and the war in Ukraine is a decision “not taken lightly”.
He added: “However, the public rightly expect government to be conducted properly, competently and seriously.”
Boris Johnson is under pressure after top ministers including Sunak resigned, following Sajid Javid who quit his role as secretary of state for health among a raft of other protest resignations from his own party.