"In light of Mr Joyce's decision to step down from the ministry, I've concluded that there is little to be gained from continuing this investigation," the letter from the Secretary of the Department of Prime Minister and Cabinet Martin Parkinson said.
"The audit into the use of travel and travel-related expenses by Mr Joyce and Ms Campion by the Independent Parliamentary Expenses Authority is ongoing."
Prime Minister Turnbull had asked Mr Parkinson on February 21 to provide advice on Mr Joyce's actions as Deputy Prime Minister.
"The Prime Minister obviously wished to have Dr Parkinson's advice on whether or not there has been a breach of the standards," deputy secretary Stephanie Foster told a Senate hearing on Monday.
Under questioning during a Senate estimates hearing, the Special Minister of State Mathias Cormann maintained no one in the government's highest ranks knew of Mr Joyce's affair.
"Just because there are rumours going around, doesn't mean somebody knows, and that applies to the Prime Minister," he said.
"The first time we knew was when there was a picture on the front page of the Daily Telegraph of a pregnant Ms Campion."
Michael McCormack sworn in as Nationals leader
On Monday Veterans Affairs Minister Michael McCormack was sworn in as the leader of the Nationals and deputy prime minister, beating a last-minute challenge from maverick backbencher George Christensen.
Nationals MPs and senators met for a special party room meeting at 8am in Parliament House.
In less than an hour, the meeting was over. Barnaby Joyce had formally resigned, the leadership contenders had made their speeches and a ballot had been held.
The result was revealed by Nationals whip Michelle Landry, who did not disclose how many of her colleagues voted for each candidate.
The Nationals whip would not comment in detail on the leadership pitch made by George Christensen, who has recently suggested the regional party consider leaving its Coalition partnership with the Liberals.
Prime Minister Malcolm Turnbull congratulated his new deputy as they posed together for TV cameras shortly after the appointment.
"The Liberal Party has been in partnership with the Nationals for all of its life," Mr Turnbull said.
Mr McCormack said the Coalition partnership would continue "long into the future".