Sen. Benigno "Noynoy" Aquino announced his campaign in the suburban Club Filipino where his mother took her oath as president after the February 1986 "People Power" revolt against the late Marcos.
"I accept the call of the people," Aquino told supporters. "I accept the responsibility of continuing our fight for the people. I accept the challenge to lead this fight."
He announced his candidacy after his Liberal Party president Manuel Roxas II last week said he was giving up his own presidential bid to give way to Aquino's son.
President Gloria Macapagal Arroyo, who lost the support of the Aquinos over charges of corruption and election fraud, is scheduled to step down after serving more than nine years in June 2010. She is not allowed to run for re-election.
The massive outpouring of sympathy for Aquino after her death from colon cancer last month prompted supporters of her son to urge him to run for president in the May 2010 election.
A three-term congressman and an economist by training, he said if elected he would ensure that government resources are utilized efficiently, criticizing Arroyo - his former economics professor - for "forgetting what she has taught me."
Despite a patchy record during her six years in office, Corazon Aquino remains a well-loved figure and is credited with restoring democratic institutions after Marcos' 20-year strongman rule. She became a focal point for opposition to Marcos after her husband, Benigno "Ninoy" Aquino Jr., was assassinated after returning from exile in 1983.
Arroyo's spokeswoman, Lorelei Fajardo, wished Aquino "luck and fortitude."
"We need strong contenders and Noynoy has emerged as one," Fajardo said.
Rep. Teddy Casino of the left-wing Bayan Muna party expressed "openess in working with him on a platform of good governance and social reform."
"The challenge for Noynoy now is to prove that he is more than simply the son of Cory and Ninoy," Casino said.
Walls of the hall where Noynoy Aquino spoke Wednesday were covered in yellow cloth, and many in the crowd wore yellow shirts - the signature color of the 1986 pro-democracy uprising led by his mother. Standing behind him were his four sisters, still wearing black mourning dresses.
After his announcement the crowd sang the patriotic song, "Bayan Ko" (My Country) while raising their hands to show the "L" sign for "laban," the Filipino word for fight, which was the anti-Marcos dictatorship slogan.
"I want to make democracy work not only for the rich and the well connected but for everyone," Aquino said.
Former Finance Secretary Cesar Purisima, who broke with Arroyo in 2005, said Noynoy Aquino's "track record of decency" will be his "political capital" in winning widespread grassroots support from Filipinos.
"If you are a decent person, you attract decent people ... and this country will move forward," he said.
Associated Press writer Teresa Cerojano contributed to this report.