"All three of these nominees have my utmost confidence," Mattis said in a statement announcing his backing and also putting to rest rumors that his advice had not been sought on the picks.
"They had my full support during the selection process, and they will have my full support during the Senate confirmation process," the retired Marine general said.
Trump announced Wednesday that financier and former Army Reserve officer Philip Bilden is his choice to succeed Ray Mabus as the next secretary of the Navy.
Earlier, Trump had tapped former Rep. Heather Wilson, a New Mexico Republican and Air Force veteran, to succeed Deborah Lee James as secretary of the Air Force and Vincent Viola, a billionaire businessman and Army veteran, as secretary of the Army.
If confirmed by the Senate, the three "will provide strong civilian leadership to strengthen military readiness, gain full value from every taxpayer dollar spent on defense, and support our service members, civilians, and their families," Mattis said. "I appreciate the willingness of these three proven leaders to serve our country."
Earlier Wednesday, Mattis made his first public remarks as defense secretary at the Pentagon's annual tribute to the late Dr. Martin Luther King Jr.
"It's an absolute delight to be back here among you again" and especially at a ceremony to honor the civil rights icon "who stood for something in our memory and our hearts," Mattis said to the audience in the Pentagon's auditorium.
"Military service is the touchstone for patriots of all races, genders, creeds," Mattis said, and "our armed forces are stronger today because of the efforts of Dr. King."