Attorneys for both sides were putting the final touches on the deal Wednesday that would allow Jeff Vanderbeek to sell his majority ownership to Harris, said the person, who asked not to be identified because neither party had announced the deal.
The Devils announced early Wednesday evening that they planned to hold a major news conference Thursday at 11 a.m.
Under NHL rules, the sale of the team could not be announced unless it had been approved by the league's board of governors.
The financially-strapped Vanderbeek has been looking for a buyer for some time. Harris emerged as the front-runner in the past week after a deal with a group led by Philadelphia attorney Andrew Barroway fell through.
Harris is the co-founder of Apollo Global Management, one of the world's largest private equity firms. He heads a group that includes another equity investor, David Blitzer.
While Harris owns the 76ers, he leases space at the Wachovia Center from Comcast Spectacor, which also owns the NHL's Flyers.
Having the lease at the Prudential Center, Harris has a chance to earn money from concerts and other events, and he might leverage "The Rock" as a way to get a better deal in Philadelphia.
There has been a little concern in Philadelphia that Harris might consider moving the 76ers from Philadelphia, which is the league's fourth largest market.
NBA Deputy Commissioner Adam Silver downplayed that suggestion.
"Josh Harris and his Sixers partners, like the NBA, love and are committed to Philadelphia," Silver said in a statement sent to The Associated Press.
Newark Mayor Cory Booker, who won the Democratic primary Tuesday for October's special U.S. Senate election to fill the seat of the late Frank Lautenberg, was excited about the prospect of the Devils having a new owner.
"We have one of the most successful arenas in America in terms of how many people are coming every year, how many concerts we're having, I'm thrilled about our arena," Booker said in a campaign stop in Hoboken on Wednesday morning. "This new owner, should it become official, Is going to be part of a great city, part of a great community, and we're looking forward to welcoming him with open arms."
A former Devils season-ticket holder since the 1980s, Vanderbeek became a minority owner of the Devils in 2000. He purchased the team and became its majority owner in 2004.
Vanderbeek was one of the leading proponents behind the building of the Prudential Center, which opened as the Devils' home in 2007. The New Jersey Nets also played at the arena before moving into a new home in Brooklyn this past season.
Forbes reported the Devils have $230 million of debt and that Vanderbeek missed the first payment on a recently restructured bank loan.
Vanderbeek did not immediately return a telephone call left by The Associated Press.
The Devils won the Stanley Cup in 1995, 2000 and 2003, and won additional Eastern Conference championships in 2001 and 2012. They missed the playoffs in the recent lockout-shortened season and were then stunned when 30-year-old superstar forward Ilya Kovalchuk decided to play in his native Russia.
The Devils moved to New Jersey in 1982, playing at the Meadowlands after relocating from Colorado.
Associated Press correspondent Katie Zezima in Hoboken contributed to this report.