His sister, Aishat, announced the wedding.
The celebrations took place in Akhmat-Yurt, the Kadyrov family's ancestral village.
High-ranking guests from the Middle East received invitations.
It was previously reported that he had entered into a religious marriage with the daughter of a Chechen senator.
Adam became famous after beating a detainee in a pretrial detention center.
He later received state awards and a position on the Chechen Security Council.