Reserve halfback Eaton was withdrawn from Sunday's match against the Waratahs in Sydney and flew across the Tasman after his 25-year-old wife Hannah was killed when the BMW she was driving collided with an SUV near Thames on Saturday.
A passenger in the other car suffered serious injuries.
Eaton, who is on a short-term Super Rugby contract with the Perth-based Force, took to Twitter to thank friends and fans for their support for him and their young daughter Layla.
"i love my wife so much it hurts. my angel layla is my world and is the last thing holding me together. love 2 all," he wrote.
All Blacks Piri Weepu, Victor Vito and Neemia Tialata were among those sending condolences to Eaton, their 28-year-old former teammate at the Wellington-based Hurricanes.
"My thoughts and prayers go out to you and Layla brother. Stay strong my mate. Words can never bring her back, but we here 4 you," wrote Weepu.
The Force are expected to make a statement later on Monday.