Rockwell was raised in Minneapolis, and in his early career he toured the U.S. in various rock and rhythm and blues bands. He worked in Las Vegas in the late 1960s and early 1970s, then moved to New York City, where he played with The Thad Jones/Mel Lewis Orchestra, Tito Puente, Ben Sidran, Freddie Hubbard, Ray Drummond, Billy Hart, Rufus Reid, Victor Lewis, Ron McClure, Tom Harrell, Chuck Israels, John Hicks, Al Foster, Anthony Cox, Bill Dobbins, Keith Copeland, Clint Houston, and Richie Beirach.

After settling in Copenhagen, Rockwell released a large number of albums for SteepleChase Records. He has worked in Europe with Ernie Wilkins, Kenny Drew, Alex Riel, Marilyn Mazur, Kenny Wheeler, Jan Kasperson, and Jesper Lungaard.