Duggar's parents, Michelle and Jim Bob, also congratulated their son and new daughter-in-law on their big day.
"We are so happy for Joe and Kendra! It was a beautiful wedding and we look forward to many wonderful memories in the future!" the parents said in a statement.
The lovebirds met through church and began their courtship in March. In May, Duggar proposed to his girlfriend on the same night his older sister, Joy-Anna, married Austin Forsyth.
At the time, Caldwell shared that their engagement is different from their courtship in that they can hold hands and say "I love you" and that they were looking forward to being able to minister together.
Duggar and Caldwell recently went on a mission trip to Panama, where they partnered with local missionaries, shared their faith, and helped build a church building.
For more on the couple, watch below!