Deschanel's screen credits include "Yes Man," "The Happening," "Elf" and "The Good Girl."
Gibbard is the front man for the band Death Cab for Cutie.
The source said Deschanel and Gibbard are "so thrilled" about their betrothal.
"Zooey was swept off her feet, and Ben is so excited," the insider told Usmagazine.com.
Celebrity Families of 2014 [PHOTOS]