Muir is expected to coach the backs, while Stormers assistant and former London Irish coach Gary Gold will coach the forwards in the Test series against Wales next month.
"I am delighted with the coaching team we have assembled," said De Villiers in a statement. "Gary and Dick have fine pedigrees and I have been very impressed in my previous dealings with them.
"I am looking forward to working with them."
Charles Wessels (logistics manager), Dr Craig Roberts (team doctor), Renee Lombard (physiotherapist), Neels Liebel (conditioning coach), Philip Malakoane (baggage master) and Chris Hewitt (communications manager) complete the team.
The role of team manager has yet to be filled.
"We are confident that we have assembled a very good management team," said Professor Jannie Ferreira, who led the recruitment process.
"It took some time before we could make the formal announcement but they have been hard at work as a team behind the scenes for some time now."
Muir took the Sharks to the Super 14 final last year, where they lost in the last minute to the Bulls, and has a chance of making the semi-finals in this year's competition as well.
As one of the most respected tactical analysts in the game, Gold is renowned for his academic and precise approach to coaching.
A former coach of Western Province, he will continue as an assistant coach with the Stormers to the end of the 2010 season.