According to the author of 1 Kings, when Rehoboam died, he was buried in the place where his ancestors were buried, in the city of David. After he died, his son Abijam became the new king.
1 Kings 14:31: And Rehoboam slept with his fathers, and was buried with his fathers in the city of David. And his mother's name [was] Naamah an Ammonitess. And Abijam his son reigned in his stead. [Abijam: also called, Abijah: Gr. Abia]
1 Kings 14:31 states that Rehoboam was buried in the city of David, and his son Abijah reigned in his place. In 1 Chronicles 3:10, Rehoboam's son is listed as Abia, showing a variation in name.
1 Chronicles 3:10: And Solomon's son [was] Rehoboam, Abia his son, Asa his son, Jehoshaphat his son, [Abia: or, Abijam]