The pair first met in 2012 while filming Lars von Trier’s NC-17 drama Nymphomaniac: Vol. II, and Goth later appeared in a music video LaBeouf directed in 2014.
The apparent wedding comes after a roller-coaster year for the young couple, which included a public altercation in Germany that was caught on camera last summer.
But things seemed to be looking up for LaBeouf and Goth’s relationship when they were spotted sharing a kiss in the middle of a Los Angeles crosswalk back in January.
Recently, LaBeouf, 29, appeared in the thriller Man Down alongside Kate Mara, and has also taken part in a series of bizarre art installations, including one project in which he rode an elevator for 24 hours.
Meanwhile, the London-born Goth has appeared in Everest alongside Josh Brolin, and recently starred in the horror film A Cure for Wellness with Dane Dehaan.