The couple was grabbing groceries at Gelson's earlier this month when LaBeouf, 29, told the cashier that they were set to get married, reported Us magazine.
Goth has been spotted wearing a large diamond ring on her wedding finger, and last month, Labeouf called the actress his fiancee while executing his performance art project #Elevate, during which he rode an elevator with strangers for an entire day.
The couple met and fell in love while shooting "Nymphomaniac: Vol II" in 2012. Engagement rumours have been spiralling around the pair ever since the British actress appeared to be wearing an engagement ring at a 2015 Paris Fashion Week show.
LaBeouf previously dated stylist Karolyn Pho and another British actress, Carey Mulligan.