Wyllie had a four-year stint with the South American side from 1995-1999. He started as an assistant coach responsible for the forwards and was head coach in 1999.
The Rugby Paper, in its obituary of Wyllie, noted, "For some time Argentina had been blessed with abundant but unrealised talent, it was Wyllie that brought nous and practicality to proceedings while he would have nothing to do with the internal politics that had bedevilled team selection.
"This process culminated with their historic World Cup quarter-final play-off win over Ireland in Lens. Everything good and positive in modern-day Pumas rugby flows from that moment, and Wyllie played a huge role in getting Argentina fit for purpose.
"He was in passing – contrary to the general perception – a joy to work with media-wise.
"The gnarled Kiwi formed a close bond with the young Agustin Pichot, who was then seen, by some in Argentina, as a mercurial and inconsistent talent who had disappeared to Europe to cash in playing professionally.
"Wyllie begged to differ and also saw Pichot's potential as a leader. He backed his man to the hilt during 1999 when some even argued that Pichot should be axed from the squad and he continued to back him from afar in the years that followed.
"He flew from New Zealand to France to attend Pichot's last ever game in 2009 while he always spoke up in support of Pichot when the Argentinian attempted to scale the greasy pole of rugby politics with World Rugby."
Pichot paid tribute to Wyllie and said he was 'the founder of Argentine modern rugby.'
"Wyllie taught me about loyalty, love and commitment. I will never stop being grateful for what he did to me, for all of us in those moments when we were lost and for Argentina rugby."