The 51-year-old Bettencourt was previously assistant coach of the small island nation team, who were one of the revelations of the tournament in North America, going out in extra time to Argentina after getting past the first round on their debut.
Bettencourt has worked with the team over the last six years.
No details of any contract terms were announced by the Cape Verdean FA.
Bubista left the job after the World Cup to take over at Renaissance Berkane, the Moroccan club who reached the African Champions League semi-finals last season.
Cape Verde begin the 2027 Africa Cup of Nations qualifiers next month away to Mali on September 25 and host Rwanda four days later.