The LaLiga outfit will pay an initial €6 million ($6.3m) to sign Cardoso. As part of the deal, Internacional will earn 20% from any future transfer of the player.
The 22-year-old will leave Internacional at the end of the 2023 Brazilian season and sign a five-year contract with Betis, sources said.
Cardoso has scored two goals in 46 appearances in all competitions for Internacional this season. He broke into Internacional's first team in January 2020 and earlier this year extended his contract with the Porto Alegre-based club until December 2026.
Born in New Jersey to Brazilian parents, Cardoso opted to represent the United States and has made nine appearances for the senior national team.
Betis, coached by Manuel Pellegrini, are ninth in LaLiga with three wins and two defeats in 10 games.