The 25-year-old actress met Holbrook on the set of 'Very Good Girls' in 2012 and had started dating shortly after. The couple apparently are set to tie the knot soon, reported Us magazine.
"They've been by each other for a while, taking a lot of couple time," a source said.
The duo reportedly moved-in together after few months of dating, taking their relationship to the next level.
"They moved into a place in Brooklyn a few months ago," the source added.
Olsen's older sister Mary-Kate, 27, had also fuelled engagement rumours with boyfriend Olivier Sarkozy, 44, about two weeks ago, when she was spotted with a diamond sparkler on her ring finger.