"He was a great guy and cute, but it didn't work out," an insider told US Weekly of the millionaire businessman, CEO of luxury eyewear brand Oliver Peoples.
It first emerged that Ashley, 27, was dating David in September. Her representative has made no comment on the split.
The former child star has always been low-key about her relationships; her last high-profile romance was with Hangover actor Justin Bartha, between 2008 and 2011. She has also been linked to designer Greg Chait and restauranteur Scott Sartiano.
Ashley and her twin sister Mary-Kate - who is currently dating Oliver Sarkozy, half-brother of former French president Nicholas Sarkozy - first found fame starring in sitcom Full House.
They are now hugely successful designers, and have built up a fashion empire worth an estimated $1 billion.