Zivcic died at St. Michael’s Hospital just after 12:30 p.m. ET, surrounded by immediate family.
"He died in the line of duty doing his job, trying to keep the public safe," Deputy Chief Peter Sloly said.
Zivcic, 34, suffered severe head injuries after his unmarked police vehicle was involved in a collision Saturday afternoon near Bloor Street West and Neilson Drive.
Officers from around Toronto, Hamilton held vigils at the hospital Sunday. Since his death Monday, city officials, and members of various police forces and the public have been offering praise and their condolences.
Toronto Mayor Rob Ford also expressed his sympathies.
“He worked very hard and that’s why we have to support front-line police men and women. They sacrifice their life day in and day out, and it’s a very sad day today," said Ford.
Zivcic was from from St. Catharines, Ont., and had worked at Toronto's 22 Division. He was described as a “greatly respected guy.”
"It’s a terrible day for the Toronto Police Service," said Toronto Police Association president Mike McCormack.
"Our hearts are broken for John’s family."
The officer is survived by his mother, and his brother and sister and their spouses.
Hours after Zivcic died, a news release said his organs will be donated.