Manzambi scored three goals and provided two assists as Switzerland reached the World Cup quarter-finals for the first time since 1954 before losing 3-1 to Argentina.
Manzambi joined Freiburg's youth academy in 2023 and was promoted to the senior team a year later. He went on to make 58 appearances for the Bundesliga club, scoring nine goals.
He played a key role in Freiburg's run to their first major European final as the German side finished runners-up to Villa in the Europa League.
"Manzambi will take the No.44 shirt, the number he wore for the Bundesliga side when he faced Villa in Istanbul," the club said in a statement.
Aston Villa open their Premier League campaign at Brighton on August 23rd.