The 2021 second-round pick will be via the Toronto Raptors, sources said.
This is the first trade of Detroit general manager Troy Weaver's tenure and the start of his beginning to gather assets and picks to rebuild the Pistons' talent base.
Brown, 24, is a tough, defensive-minded guard who's expected to be a part of the Nets' backcourt rotation. A second-round pick in 2018, Brown started 99 games in his first two NBA seasons.
Musa, the 29th overall pick in the 2018 draft, struggled to find traction with the Nets, but he is still only 21 years old.
The NBA's moratorium on transactions will be lifted at noon ET Monday, after which this deal can be made official.