Johnson, currently an analyst on ESPN, confirmed to the network he will be taking the reins of the NBA's worst team, which finished with a 12-70 last season.
"We've come to a verbal agreement and hopefully the Nets will have an official announcement (Thursday)," Johnson said. "But, yes, I am headed to New Jersey. You look at a team that won 12 games, so the sky's the limit. There's so many great possibilities and so much potential here."
Johnson, 45, was fired by Dallas after the Mavericks exited in the first round of the 2008 NBA Playoffs. He was spurned this week in a bid for New Orleans Hornets head coaching job.
Johnson produced a 194-70 record in three-plus seasons with the Mavericks, but was only 23-24 in the post-season, dropping 12 of his last 15 playoff games.
The Nets fired head Coach Lawrence Frank Nov. 29 and then-General Manager Kiki Vandeweghe took over for the rest of the season.
New Nets owner Mikhail Prokhorov ousted Vandeweghe last month.