"We are so excited to be engaged and look forward to a lifetime together. We are so grateful for how the Lord brought us together, and we look forward to this special time of engagement and to someday serving Christ as man and wife," the couple said in a statement.
The 22-year-old Counting Up star and Caldwell, 18, also shared a video announcement on TLC.com, describing how their engagement came together.
"We got engaged," Duggar says. "I asked Joy and Austin a few weeks ago if they would mind if I proposed to her at [their] wedding and they were like, 'Oh yeah, we'd love it if you do that.'"
The couple met through church and began their courtship in March. Caldwell added that their engagement is different from their courtship in that they can hold hands and say "I love you." They also look forward to being able to minister together.
Joseph's parents, Michelle and Jim Bob Duggar, also shared sweet words about their son's big news.
"There is a lot of love in the air today! We are so pleased to announce that Joe and Kendra are now engaged to be married! Our sweet Joe is on the verge of starting his own family. We are so happy for them both," they wrote. "Above all, we are so thankful for their love and commitment to Christ. We are so excited about another Duggar wedding in the near future! We know wonderful days are ahead for Joe and Kendra and we are looking forward to every moment! Our entire family rejoices!"