Arroyo spent three seasons at Oregon, where he also served as assistant head coach and quarterbacks coach.
"Marcus has demonstrated a commitment to integrity and excellence throughout his career, and we look forward to a bright future for our football program under his leadership," UNLV president Marta Meana said. "We're excited to welcome Marcus and his family to Las Vegas and UNLV."
Oregon scored 35.9 points per game and Justin Herbert was among college football's top quarterbacks under Arroyo.
The 39-year-old played quarterback at San Jose State from 1998 to 2002 and later coached the Spartans' signal-callers from 2006 to 2008.
It was reported Tuesday that Louisiana State defensive coordinator Dave Aranda was offered the top job at UNLV, but a source told Mark Anderson of the Las Vegas Review-Journal that the school was, at the time, yet to finish vetting its head-coaching candidates.
The Rebels fired Tony Sanchez on Nov. 25 after five seasons. He put together a 20-40 record.