She died yesterday at the National University Hospital, where she had been undergoing treatment for leukaemia since February this year.
Mrs Yudhoyono had been a pillar of strength for her husband during his two-term presidency, between 2004 to 2014.
Prime Minister Lee Hsien Loong said in a Facebook posting that his wife Ho Ching and himself were dear friends of Mrs Yudhoyono.
"Her commitment to service and to helping fellow Indonesians were an inspiration to many. She touched the lives of many," he said.
Mrs Yudhoyono's remains were flown from Paya Lebar Air Base to Indonesia's Halim Perdanakusuma Airport in East Jakarta, and from there to her home in Cikeas, Bogor, in West Java.
She will be buried at the Kalibata Heroes Cemetery in Jakarta today.