The Full House star, 27, was photographed with Miller as he attended the funeral of his tragic Capote star Philip Seymour Hoffman in New York last Friday (07Feb14), and now editors at UsMagazine.com reveal they have been a couple for several weeks.
A source tells the website, "They were introduced and have started dating."
Insiders claim Olsen also paid a visit to the 47-year-old filmmaker in Los Angeles last month (Jan14), as he worked on his upcoming movie, Foxcatcher.
The news emerges just four weeks after it was revealed that Olsen, who previously romanced The Hangover star Justin Bartha, had split from fashion boss David Schulte after less than a year together.
Olsen and her twin sister appear to have a thing for older men - Mary-Kate Olsen has been in a relationship with 44-year-old businessman Olivier Sarkozy, the half-brother of former French president Nicolas Sarkozy, since 2012.