The Belgium international, 26, will join the club on 1 July, after his Leicester contract expires.
Following Leicester’s relegation from the Premier League, Arsenal, Manchester United and Roma were also rumoured to be interested in Tielemans.
Tielemans – expected to be Villa’s first signing of the summer – joined Leicester in 2019 and helped the Foxes win the FA Cup in 2021.
The Belgian scored the only goal in Leicester’s 1-0 victory against Chelsea in the final. That was one of 28 goals he scored for the club in 195 appearances across all competitions.
Tielemans joined Leicester initially on loan from Monaco in January 2019 and his move was made permanent in a then club-record £40m deal in July of that year.
He has also played at two World Cups, in 2018 and 2022, as well as Euro 2020.
Tielemans joins Villa after they finished seventh in the Premier League last season, securing qualification for the Europa Conference League.