Arniel, who spent four the past four seasons coaching the American Hockey League's Manitoba Moose, replaces interim coach Claude Noel.
He takes over a Columbus team that finished second-last in the NHL's Western Conference last season after making the playoffs the in the prior season.
"I've been impressed by a lot of what I see here," he said after signing a three-year contract with Columbus. "I see myself as a young coach and this is a young, talented team with great potential. I am ready to get to work."
Noel took over as interim coach in February after Ken Hitchcock was fired.
(Writing by Mark Lamport-Stokes in Los Angeles; Editing by Frank Pingue)