Lorenzo, 57, has led Broward's fire department since 1999.
Before that, he served as the top fire official in Hialeah and Hollywood.
Flanked by dozens of well-wishers in the commission chamber Tuesday, Lorenzo promised to work hand-in-hand with labor and keep a watchful eye over Miami-Dade.
''I married here, had my children here and my grandchildren. I love this county,'' Lorenzo said.
Lorenzo will replace acting chief Antonio Bared, who is retiring at month's end.
Among the audience members were Hialeah Mayor Raul Martinez, Broward Sheriff Ken Jenne, and former Miami fire chief and city manager Carlos Gimenez.
Martinez said he's known Lorenzo since childhood.
''Mr. Manager,'' the Hialeah mayor said, ``you have a great selection.''
Jenne, addressing Burgess, pretended to be angered: ``I'm going to arrest him for grand theft if he ever comes to Broward County.''
The choice was lauded by Teresa Everett of the International Association of Black Firefighters, who thanked Burgess for including her group in dialogue.
''We're extremely pleased with his Lorenzo's responses, and embrace the opportunity to move forward,'' she said.
Miami-Dade fire rescue is the seventh-largest fire department in the country with an annual budget of more than $200 million.
More than 1,800 employees, 1,600 of them uniformed officers, work for the department
