Schwarz, a highly regarded pediatrician lured from Children's Hospital of Philadelphia, has been a leader in the city's efforts to combat homelessness, obesity, and smoking.
Schwarz also was deputy mayor for health and opportunity. Two people were named Friday to fill his roles.
"The city is a better place and our children are safer because of Don Schwarz," Nutter said, sparking a standing ovation.
Ambrose took over the Department of Human Services when the child welfare agency was in disarray after the death of Danieal Kelly, a 14-year-old with cerebral palsy under the care of DHS and a social-service agency it funded.
Four employees of the outside agency were convicted of health-care fraud and conspiracy charges related to Kelly's death.
Ambrose lowered caseloads and improved services. By 2010, a panel appointed to monitor DHS reported "sea changes" at the agency.
The final departing member of Nutter's team, Suzanne Biemiller, has been prominent in City Hall for years, handling a large portfolio of the mayor's priorities.
She served stints as interim chief of staff and director of policy, planning, and coordination, and she helped develop Nutter's environmental master plan, Greenworks Philadelphia.
Most recently, as first deputy chief of staff, she has worked closely on the controversial proposal to sell the city-owned Philadelphia Gas Works to a private utility.
The departures are part of the cycle of any administration. Nutter cannot run again, and he leaves office in January 2016.
They also mark the end of a remarkable run of continuity. Nutter has not lost such high-level confidantes since his first chief of staff, Clarence D. Armbrister, stepped down in 2011.
Nutter said none of the three was looking for new work - each was recruited to a prestigious job.
Schwarz will leave July 15 to join the Robert Wood Johnson Foundation; Ambrose on Aug. 1 to join the Casey Family Programs, a foundation focused on foster care; and Biemiller on July 7 to become chief of staff for the American Board of Internal Medicine.
Schwarz's deputy mayor duties will be taken over by Susan Kretsge, the chief of staff for the city's Office of Health and Opportunity; the new health commissioner will be James Buehler, a physician and public health professor at Drexel University.
Ambrose will be replaced by Vanessa Garrett Harley, the deputy commissioner for DHS's Children and Youth Division.
No replacement was named for Biemiller.
Biemiller recalled six years ago telling her now teenage daughters that she "wouldn't have as much time to be your mom," but she wanted to help create a city where they would want to live and work.
"We don't do these jobs for the money . . . the family-friendly hours, or the stress-free work environment," she said. "We do these jobs because we believe Philadelphia is a great city and that its best days are ahead of it."