Collier has been with the Dolphins for 10 seasons, the first four as a defensive assistant.
"I think success is in the details," Collier said. "I hope whatever we do as an offensive staff, that shows up as time goes on. I don't want to leave too many things to chance."
Miami is the seventh NFL coaching stop for Trestman, who has been offensive coordinator for Arizona, Cleveland, and San Francisco. He also had assistant stints with Detroit, Minnesota, and Tampa Bay.
The New York Jets also got into the hiring act by naming Donnie Henderson defensive coordinator, as expected.
Henderson, secondary coach for the Baltimore Ravens since 1999, replaces Ted Cottrell, who was fired after the Jets' 6-10 regular season.
Jets coach Herman Edwards interviewed many candidates over the past month, with several taking jobs elsewhere. Edwards said Henderson was the third candidate interviewed and "moved up the charts real fast."
"There might be people thinking he was the last guy we wanted to hire," Edwards said. "But not in my mind. He went to the top of the list after being third candidate in here."
Henderson, a college assistant for 15 years before joining the Ravens, never has been a coordinator but has experience rebuilding a defense.
Finally, the Buffalo Bills hired Tyke Tolbert as receivers coach.
Tolbert spent last season with Arizona as the Cardinals' receivers coach, his first coaching job in the NFL. Before that, Tolbert spent nine seasons at the college level.
Tolbert replaces Fred Graves, who was hired as receivers coach by Cleveland last week after spending three years with the Bills.
Giants add staff