By Agence France-Presse
"It breaks my heart to tell everyone that Jarrod is no longer with us," she said in a statement.
The former US PGA Tour player, who had children aged six and two, passed away on Wednesday evening surrounded by family and friends.
"Lusi, Jemma and I are filled with grief and now must confront our lives without the greatest husband and father we could ever have wished for," added his wife.
Lyle moved into palliative care last week to see out his final days, saying his body could not "take anymore" after acute myeloid leukaemia returned for a third time.
His plight touched fans and players around the world, with goodwill messages pouring in from across the globe.
"Jarrod was able to take in many of the unbelievably kind and generous acts and words in his final few days and was overwhelmed by the emotional outpouring," said Briony.
"He asked that I provide a simple message: 'Thanks for your support, it meant the world. My time was short, but if I've helped people think and act on behalf of those families who suffer through cancer, hopefully it wasn't wasted."
Lyle overcame leukaemia as a 17-year-old before suffering a recurrence in 2012.
He won that battle and made his return to professional golf at the Australian Masters in November 2013. But his health deteriorated again in recent months.
Lyle joined the PGA Tour in 2007 and managed a handful of top 10 finishes.