The 48-year-old will move to Thomond Park from Canterbury, where he has been head coach since 2006, and replace Tony McGahan, who is taking up a coaching co-ordinator's role with the Australian Rugby Union.
Penney will take charge of the New Zealand Under-20 squad for this summer's World Cup in South Africa, before starting his Munster duties during July.
Penney guided Canterbury to their fourth straight national provincial title last season, and he has previously served as Canterbury Crusaders assistant coach during a successful Super 12 campaign.
"We conducted a thorough search to find a replacement for Tony McGahan and were delighted with the calibre of the candidates," Munster chief executive Garrett Fitzgerald said.
"Rob Penney's record speaks for itself, and we look forward to welcoming him to Munster."