Vidal died in his sleep in France.
A former top triathlete, he had been forced to quit competing after suffering an earlier heart attack in 2014.
His death led to mourning throughout the New Zealand and French sporting communities.
On the day of his funeral, New Zealand triathlete Kris Gemmell tweeted: "Time 2 say farewell until we meet again! I'll take great pleasure talking about how you change my life.
"Miss u bro, take care until we meet again."
The statement released by Tri NZ on Saturday afternoon said "Andrea Hewitt is training at her customary intensity which she built with the late Laurent Vidal".
In the statement Pilot said: "The circumstances in which I find myself coaching Andrea are obviously tragic, and yet I am honoured and humbled to be working with Andrea and her team to carry on the work of Laurent.
"We are already very focused on continuing to provide the best training programme and build up for Andrea to enable her to deliver her best performance at the Olympic Games in August."
Triathlon New Zealand High Performance Director Graeme Maw welcomed Pilone to the team.
"Chris is vastly experienced in both triathlon and athletics, we look forward to having Chris work with Andrea towards Rio and help her achieve her goals at the Olympics. Tri NZ High Performance Lead Coach Jon Brown will continue to work closely with Chris, just as was the case with Laurent previously. The priority is and always has been Andrea as we continue to support her and the team around her towards Rio, as is the case with all of our HP athletes."
Hewitt is training with local and international triathletes who are currently based in Christchurch.
She was silver medallist in the 2015 ITU World Triathlon Series, her fifth World Championship medal. The Cantabrian is already qualified and named to the New Zealand team for Rio - she was the first athlete from any sport to be officially named for the Games in October last year.