In a recorded three-minute statement released by his brother's campaign team, a gravelly-voiced Ford first thanked well-wishers, saying their support meant the world to him and his family.
"With the love and support of my family, my friends, and the people of Toronto — I will beat this," he added.
"I am determined to face this head on and return strong for my family and for my city."
Ford was diagnosed Wednesday with malignant liposarcoma — a type of cancer that arises from fat cells and can attack a variety of soft tissues. His doctor said he will be undergoing two rounds of chemotherapy before they determine the next step in his treatment.
His brother entered the mayoral race after Ford withdrew his bid for re-election last Friday, opting instead to run as a councillor in the same ward he represented for a decade before being elected to the top job in 2010.
He urged voters Thursday to rally behind Coun. Doug Ford, who has yet to officially launch his campaign.
His brother was by his side, sharing his vision for the city, helping him accomplish what he set out to do as mayor, Ford said. Doug is "prepared to tackle the issues head on," he added.
"I'm encouraging my brother to jump into this race wholeheartedly, right now," Ford said.
"You, the people of Toronto, have been with me since Day 1. Now I ask you to throw your support behind my brother Doug."
Speaking to reporters outside the hospital, Doug Ford said he would hit the hustings in earnest on Friday.
"We already have a solid team from what Rob has built and we just look forward to starting this campaign and getting out there," he said.
One expert was skeptical that the ill mayor's endorsement of his brother will boost support even among Ford's followers.
"I just don't think that we can expect that all those people are going to listen to that and move over, because their connection with Rob was an emotional connection," said Henry Jacek, a political science professor at Hamilton's McMaster University.
"In a sense, he's making from his point of view a rational argument: you should vote for my brother because he's just like me. But their connection with him is an emotional one, and I'm not so sure these people will respond to a rational argument, even from that person they've got an emotional bond with."
Ford's recording is not unlike the public letter former federal NDP leader Jack Layton's penned on his death bed in 2011, he said.
"We see people sometimes with illness, but they're still fighting politically as they go down," Jacek said.
"Some people, for whom politics is so terribly important, they feel so strongly about, they're delivering that political message right to the very, very end."
Another observer said the Fords' determination to keep the family in the political arena could end up alienating their base.
"I think there is a part of the idea that they're creating a family dynasty and that may actually undermine some of their populist appeal," said Peter Graefe, who also teaches political science at McMaster.
Before withdrawing from the race, Ford said this month he planned to hold on to the mayor's seat for another 14 years, which "begins to make it look like he feels he's owed a place in elected politics," Graefe said.
"There's a certain sense of entitlement to it that runs counter to their populist claims and begins to make them look like part of the elite."
News of Ford's cancer made headlines around the world and has drawn expressions of sympathy from politicians of all stripes, including Prime Minister Stephen Harper.
Ford — who has turned into an international celebrity due to a series of scandals touched off by reports of a video appearing to show him smoking crack cocaine — returned to office just over two months ago after a stint in rehab for substance abuse issues.
His role as mayor has been largely symbolic since last November, when he was stripped of most of his powers following his admissions of alcohol abuse and drug use during "drunken stupors.''
_ With files from Paola Loriggio.