Former speaker of Singapore's parliament, Halimah Yacob, arrives to submit her presidential nomination papers at the nomination centre in Singapore on September 13.
Yacob is Singapore's first ethnic Malay president in 47 years.
The returning officer declared Halimah Yacob, 63, elected on Wednesday after nominations closed.
Of the four other applicants, two were not Malays and two were not given certificates of eligibility, the elections department said earlier this week. Halimah had automatically qualified because she held a senior public post for over three years.
Yacob was competing with Salleh Marican and Farid Khan, whose applications were turned down for failing to meet the nomination's criteria.Candidates from the private sector were required to have led a company with shareholder equity of at least Dollars 372 million.
The prime minister's office said it had no comment on criticism of the election process.
Also, Association of Women for Action and Research (AWARE), a rights group, in a statement said Yacob's victory had not reflected their hopes.
"[We hope] more will be done to improve access to politics for all of Singapore's women".
Yusof was president between 1965 and 1970, the first years of Singapore's independence following a short-lived union with neighboring Malaysia, but executive power lay with Lee Kuan Yew, the country's first prime minister.
In the 2015 general election - held months after the death of Lee Kuan Yew - the PAP won nearly 70 per cent of the popular vote and swept all but six of parliament's 89 seats.
Yacob is expected to be sworn into office on Thursday. "I'm a president for everyone".
Asked yesterday about the backlash, Mdm Halimah said: "Whether there's an election or no election, my promise is really to serve everyone ... I will serve with great vigour, with a lot of hard work, with the same passion and commitment that I have served people with for the last four decades".