Zahawi, who was the education secretary, was named by Johnson as the chief executive of the treasury.
Johnson earlier appointed Steve Barclay as the new health secretary after Sajid Javid resigned from that position.
Sunak and Javid resigned from the government Tuesday evening, minutes apart from each other.
In the forced reshuffle, Michelle Donelan has been named the new education secretary, replacing Zahawi.
The backdrop to the two high-profile resignations came after a scandal over Chris Pincher, a government lawmaker who resigned as the deputy chief whip last week after allegations about an incident that occurred at a private members’ club.
Downing Street initially said that Johnson was unaware of previous specific allegations against Pincher, but it later emerged that he was in fact informed when he was foreign minister in 2019 of previous instances of alleged misconduct on Pincher’s part.
Just before the resignations, Johnson apologized for appointing Pincher as the deputy chief whip.