Burton is perhaps the standout signing of the four, having featured for Italy in last month's Six Nations. The 32-year-old Italian was born in Australia and is currently with Italian side Treviso.
As well as helping to gain 21 caps for Italy, Burton's experience has helped Treviso to seventh place in the RaboDirect PRO12 this season leaving Edwards to hope he can have a similar impact at Rodney Parade.
"Any team who has played against Kris knows how influential he can be on a game with his goal kicking and tactical awareness," he said.
"Alongside the recruitment of Richie Rees, we now have a good blend of young and experienced half-backs. It gives us the opportunity to generate competition and allows us to create combinations that can be influential and exciting for the team."
Fellow new signing Muller will offer the Dragons extra forward power, the lock joining from Super 15 side the Cheetahs. The South African made his Super rugby debut with the Stormers in 2009 and is known for his superb lineout skills and physical work ethic.
And with the potential of Muller to partner Wales man Andrew Coombs at lock next season, the Dragons won't lack for mobility or power in the engine room.
"Martin is a player whose progress we have been following carefully for a couple of seasons," added Edwards.
"We recognise he is a player of great pedigree and potential and possesses the attributes that will suit the way we want to play."
Backrower Talei brings a wealth of experience from his time with Edinburgh and Worcester and has previosuly impressed in the Heineken Cup.
Prop Chapparro meanwhile, has recently been capped by Argentina, featuring for the Pumas against France and Italy.
"We believe he will provide a positive influence on our current front row,' said Edwards of the 23-year-old prop.
"The quality of Argentinean front row forwards and in particular their technique in the scrum is recognised worldwide."