Mr Johnson’s predecessor asked why the prime minister had given the job to a “political appointee with no proven expertise” in the area.
Ms May told Michael Gove, the chancellor of the Duchy of Lancaster and her former cabinet colleague, that she served on the National Security Council for nine years, including as prime minister, and during that time had listened to the expert independent advice of national security advisors.
In a dig at her successor’s decision, she asked why the job has now gone to a “political appointee with no proven expertise in national security.”
Just hours earlier another former Tory leader William Hague said that the decision sat “uneasily” with the desire for top officials to be highly knowledgeable about their areas of responsibility.
Unlike previous holders of the post, David Frost, currently Mr Johnson's chief EU negotiator, is a political adviser rather than a career civil servant.
He replaces Sir Mark Sedwill, who announced earlier this week he would stand down from the role, and his other job as cabinet secretary, amid reports of a falling out with Mr Johnson's chief adviser Dominic Cummings.
Mr Gove defended Mr Frost’s appointment, saying he had been a “distinguished diplomat” before a series of other roles, including with the Scotch Whisky Association.
Mr Gove told MPs: "We have had previous national security advisers, all of them excellent, not all of them necessarily people who were steeped in the security world, some of whom were distinguished diplomats in their own right.”
Mr Gove had been dragged to the Commons to answer an urgent question on the appointment.
Meanwhile, in his column in the Daily Telegraph, Mr Hague wrote of the decision: “Out there in our intelligence agencies, there are a lot of ‘consultant surgeons’ who have spent a lifetime performing difficult operations. You can’t pass them all over while calling for more expertise without eyebrows being raised, or indeed daggers sharpened.”
The former foreign secretary also warned that the manner of Sir Mark’s departure was “not a good example of how to lead the government machine toward positive change.”
He added that anonymous briefings on senior officials are “a reprehensible habit of the current team in No. 10,” which would prove “a disincentive for talented people to take on jobs at the top,” and “to which the prime minister should put a stop.”