A statement issued by the church said it had opted for the split so it could create its own youth programme, although the two organisations' values had clearly diverged over recent years.
The announcement was not a complete surprise after the religion last year removed 185,000 boys between the ages of 14 and 18 from the Scouts, signalling an end to a nearly century-old relationship based on shared values.
In 2015 the Boy Scouts decided to allow gay troop leaders and announced last year it would allow girls in its ranks.
Last week, the organisation said it would change the name of its flagship programme next year to Scouts BSA to account for the inclusion of girls.
Like other conservative faiths, the Mormon church opposes gay marriage and teaches that being in a homosexual relationship is a sin.
The church initially said it was "deeply troubled" by the Boy Scouts' policy change but stayed with the organisation after receiving assurances it could appoint troop leaders according to its own religious and moral values.
The religion has also traditionally used separate youth programmes for boys and girls.
The Mormon church said in a statement the new programme that will start in 2020 will "help all girls and boys, young women and young men discover their eternal identity, build character and resilience, develop life skills and fulfil their divine roles as daughters and sons of God."
The move will mean its remaining 425,000 boys will be moved into a gospel-focused youth programme it is developing.
Joining the Boy Scouts is practically automatic among Mormon boys, and the religion has long been the biggest sponsor of Boy Scout troops in the United States.
The Mormon boys who will be leaving represent about 18.5 per cent of the 2.3 million youth in the organisation.
Agencies contributed to this report