Dillard, 25, is an accountant who's been courting the 19 Kids and Counting star since November.
"I am so happy," Duggar, 22, said. "Our story is so very unique. The first time we talked, he was in Japan, we met in Nepal, he spent time in India and Israel and then came back to Arkansas where he met my family. We have a very international story even though we live so close."
Now that they're engaged, Duggar and Dillard have agreed to start holding hands, but any other physical contact will wait until their wedding day. "I feel like I'm dreaming," Dillard said. "It was great to grab her hand for the first time."
Duggar's younger sister Jessa, 21, also recently entered a courtship with Ben Seewald, 18.