Harris is expected to join John Henry (Liverpool), the Glazer family (Manchester United), Stan Kroenke (Arsenal) and Shad Khan (Fulham) as an owner of both an English football club and an American sports franchise.
The co-founder of Apollo Global Management - a private equity firm - already owns the NBA's Philadelphia 76ers and the New Jersey Devils of the NHL.
According to reports, Palace's co-chairman Steve Parish would stay and run the club for Harris, with the former widely credited for helping rebuild the London-based club since 2010, leading them back to the Premier League at the end of the 2012-13 season.
Palace own their stadium - Selhurst Park - and their training facility, after purchasing both in recent years.
Sal Galatioto, founder of Galatioto Sports Partners, who represented Comcast-Spectacor in its sale of the 76ers to Harris, told Bloomberg: "Josh obviously knows how to run pro sports franchises.
"It's a very interesting investment that should be a very good one for him over the long run.
"English Premier League soccer is arguably the best soccer in the world and it's very valuable media content. It's growing in other parts of the world, especially North America."
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