Veillette's diverse client list includes John Sebastian, James Taylor, Ani DiFranco, Dave Mathews, John Mayer, Jorma Kaukonen, Steve Miller, Todd Rundgren, Tina Weymouth, Chris Martin, Jimmy Vivino, Tim Pierce, Colin Hay, David Torn, Brian May, Kaki King, Neal Schon, Mike McCready, Eddie Van Halen and other notable players.
He took a class in guitar-making, taught by luthier Michael Gurian in 1971, to learn how to repair the broken headstock on his Gibson J-45.
He became interested in guitar building and teamed up with fellow architectural student Harvey Citron, and formed Veillette-Citron in 1976.
Veillette-Citron pioneered neck-thru-body construction, made innovations in instrument electronics, and set new trends in modern electric bass design.
He appeared on Krishna Das' 2005 album All One, featuring Walter Becker on bass, drummer Rick Allen, tabla player Ty Burhoe, and guitarist/composer David Nichtern.