Cameron said that he would meet his cabinet on Tuesday and take prime minister’s question time on Wednesday before visiting Queen Elizabeth II to announce his resignation formally.
“So, we’ll have a new prime minister in that building behind me by Wednesday evening,” he said outside 10 Downing Street, the prime minister’s residence in London.
He described Theresa May, who is set to succeed him as “strong and competent”, saying she would have his full support.
Cameron announced his resignation last month after losing in the referendum. Majority of the voters chose Britain pulling out of the European Union (EU), as against Cameron’s wish.
The prime minister had announced that he will be stepping down in October, but the withdrawal of Andrea Leadsom, the contender for the Conservative Party leadership, from the race, changed Cameron’s calculation.