"My baby love and I are ENGAGED!!! Hallelujah Hawaii!!!" Simpson, 29, tweeted.
"The love of my life said YES!!!!!!" Ross, 25, said in his own Twitter message.
People.com said the couple went public with their relationship last summer. They did not say when they plan to tie the knot.
Simpson has a 5-year-old son from her previous marriage to Fall Out Boy front man Pete Wentz.
Celebrity Couples of 2014 [PHOTOS]