Mdm Halimah was declared President-elect after her nomination papers were found to be in order on Wednesday. She will be Singapore's first female President and first Malay head of state in 47 years.
In a statement, Mr Salleh said that he believed Mdm Halimah would be a "unifying President".
"This has been a divisive run-up to the nomination for the President," the Second Chance chief said. "I hope Mdm Halimah will heal the wounds."
Mr Farid also wished Mdm Halimah all the best, and said he hoped that she would "have the people of Singapore in her thoughts when making any decisions that will affect our lives and the lives of our children".
In a statement, the Bourbon Offshore Asia Pacific chairman said that although he had been looking forward to a contest, he accepted his disqualification from the race, "but with a heavy heart and great disappointment".
"Even though I may not have the opportunity to run for this Presidency, somehow I still have gained so much and that is probably why I still feel victorious today," he said.
Mr Marican and Mr Farid confirmed on Monday that their applications to stand for President had been turned down, after the Elections Department said only one Certificate of Eligibility had been issued for the contest.
COMMUNITY GROUPS CONGRATULATE PRESIDENT-ELECT HALIMAH
In a statement issued to the media on Wednesday, the Singapore Muslim Women’s Association (PPIS) congratulated the President-elect on her new role.
Mdm Halimah has been the organisation’s patron for 13 years.
In the statement, PPIS said Mdm Halimah’s four decades of experience in public service has shaped her to be a leader who has good rapport with the people she represents.
“While Madam Halimah’s resignation as Speaker of Parliament, Member of Parliament as well as a member of the People Action Party’s Central Executive Committee, is a loss to representation of women in Parliament, PPIS believes that as the first female President to the Republic of Singapore, Madam Halimah will continue to be an inspiration to the women of Singapore, especially our future leaders, who will be encouraged to take on new challenges, embrace leadership roles and contribute to nation building,” PPIS said.
The Singapore Federation of Chinese Clan Associations (SFCCA) also sent their congratulations to President-elect Halimah Yacob.
“The breadth and depth of her experience will definitely be an advantage towards the building of our social capital for the nation’s development, as well as in championing for an inclusive and cohesive Singapore,” SFCCA said in a statement on Wednesday.
“The Chinese community is confident that under Madam Halimah’s capable leadership, Singapore will continue to prosper and progress as one united nation.”