Muggleton is a highly experienced former defence coach of Australia where he spent 10 years. He helped them to World Cup glory in 1999 and to victory over the Lions in 2001. Born in Sydney, the 48-year-old joins the Scarlets on July 1.
He said: "The Llanelli Scarlets are one of world rugby's big names and I look forward with great anticipation to helping them achieve their ambitious future goals."
Harrington is assistant strength and conditioning coach at Super 14 finalists the New South Wales Waratahs and from 2004 spent three years as strength and conditioning coach with Leinster. Born in Sydney, the 34-year-old assisted Ireland in their build-up to last year's World Cup. He joins the Scarlets this month (June) to prepare the pre-season fitness programme.
He commented: "It's a real thrill to be joining the Scarlets at such a pivotal time in their history. The new player signings, the new coaching team and the new stadium show that the region plans a big future."
Scarlets Chief Executive Stuart Gallacher added: "I'm delighted with this superb team which will help propel us into an exciting new era. John and Brad bring great vision, knowledge and skill - and we've been very impressed with Paul in his time here.
"The coaching team, along with our latest player signings and the fabulous new stadium illustrate how determined we are to thrive at the highest level of the professional game.
"I know that Nigel Davies is relishing the prospect of working with John, Brad and Paul."
Scarlets backs coach Robert Jones and fitness coach Wayne Proctor are leaving the region by mutual consent.
Gallacher said: "We thank Robert and Wayne for the work they've put in on behalf of the Scarlets and we wish them all the best for the future. Wayne has particularly strong links with the Scarlets having served us well as both a player and fitness coach."
The Scarlets are due to move into their new £23m home - Parc y Scarlets - in November. The complex features a stadium with a capacity of around 14,500 and top-grade training facilities.