The actors first appeared on the big screen together in young adult adaptation Divergent, playing Tris and her brother Caleb.
Woodley told MTV she first met Elgort at a cast dinner in Chicago for Divergent.
"I'd never heard anything about [Ansel] before meeting him on Divergent," she said.
He "was so quiet and so open and so pure. He was more observant. There was something very special about him, something that moved me," she added
Celebrity Families of 2014 [PHOTOS]