The 18-year-old, who has spent six years at the club, was named its youth team player of the year for last season, an award previously won by Ryan Giggs, Paul Scholes, Marcus Rashford and Mason Greenwood.
The winger has spent 2020-2021 with Neil Wood's under-23s side and continued to impress, with eight goals and three assists in 16 appearances.
A Sweden youth international, he is the son of Joseph Elanga, the former Malmo and Cameroon defender who played at the 1998 World Cup.
Former United captain Gary Neville described the young Elanga as "a nightmare to play against" after he impressed in a 6-1 thrashing of Salford City in the EFL Trophy last September.
Exact details of his new contract were not specified in the announcement from United.
The news of Elanga's deal came a day after United also announced a new contract for promising young midfielder Hannibal Mejbri.