The 2020 Caulfield Cup winner has been successful 11 times at the top level and connections of the mare are planning a tilt at the Prix de l'Arc de Triomphe this autumn as well as a possible bid for the Fillies & Mares Stakes on Qipco British Champions Day at Ascot.
However, the decision to move the six-year-old to the Northern Hemisphere at this stage of her career comes as something of a shock.
Verry Elleegant's owners, who include Brae Sokolski and Ozzie Kheir, said that in order to campaign in Europe properly, the horse would have to be trained abroad.
A statement, issued on Thursday morning, read: "We know she is a world class stayer who needs 2400m+ to show her true ability, but we expect her be weighted out of the Cups and as such there are limited options for her domestically.
"After much deliberation we came to the realisation that if we want to campaign her in Europe, we need to do it properly and send her to be trained and prepared in the northern hemisphere.
"As such we wish to advise that Verry Elleegant will be transferred to the care of leading French trainer Francis-Henri Graffard and trained out of the world class facilities at Chantilly.
"Although transportation arrangements are still being finalised, she will finish her spell next week and subject to flight availability will fly out anytime from that point forward.
"Bringing her to Europe early opens up a number of new possibilities, one of which is running in the Arc, however we will just keep an open mind on her program until deeper in her preparation with Francis."
The statement also paid tribute to Waller and his team, along with regular rider James Mcdonald, who steered her to victory in Australia's most famous race by four lengths on her last appearance in November.
"We would like to take this opportunity to express our enormous gratitude to Chris Waller and his team for the outstanding job they have done with Verry Elleegant.
"Chris is one of the world's greatest trainers and must take a huge amount of credit in allowing her to fulfil her potential and bringing her up to her peak, preparation after preparation," the statement added.
"We would also like to give particular kudos to her strapper, Rocky Mangat and track rider, Chris Harwood and of course James McDonald who won a staggering nine Group Ones aboard her including her crowning achievement in the 2021 Melbourne Cup.
"We are incredibly excited about the journey ahead and showcasing her on the world stage. We know win, lose or draw she will do us, Australia and of course New Zealand proud."
Waller was quick to pay tribute to the 2020/2021 Australian Racehorse of the Year, who won him a first Melbourne Cup.
He said: "It has been an honour to have trained Verry Elleegant for a major part of her career. She has given us so many great thrills over a number of years and we are very proud of her.
"My team around Australia are all responsible for her success and longevity which I thank them for and wish the owners all the very best in her Northern Hemisphere race campaign."