Mr Pillay, 83, took over from Tony Tan Keng Yam who completed a six-year term yesterday.
Mr Pillay, chairman of the Council of Presidential Advisers (CPA), will act as the President of Singapore until after polling day on September 23 - or after nomination day on September 13, if a candidate is elected unopposed.
When the office of the President of Singapore is vacant, the first in line to exercise its powers is the CPA chairman, followed by the Speaker of Parliament, The Straits Times said.
This is the first time that the office has fallen vacant since the elected presidency was introduced in 1991, according to the report.
Mr Pillay has served for more than 60 such "stints" - the longest of which was 16 days in April and May of 2007, when then President SR Nathan visited Africa.
Three candidates of Malay origins are expected to stand for election for the president's post is reserved this time for a minority group representation at the highest office of the land.