The deal with the former Memphis Grizzlies coach comes two days after the Nets made a trade with Milwaukee to allow Kidd out of his contract so the Bucks could hire him.
Nets general manager Billy King and his assistants then met with Hollins on Monday night and again Tuesday before agreeing to the deal. Terms were not disclosed.
''I want to thank the Nets ownership and Billy for this opportunity,'' Hollins said in a statement. ''It has been a long process to get back into the league, and I believe that Billy and I will have a very successful working relationship. Brooklyn has firmly established itself as a franchise that is committed to winning, and I eagerly look forward to becoming part of that culture and building on the success of the past two playoff appearances.''
The Nets will introduce Hollins at a press conference Monday.
Hollins led Memphis to 56 victories and the 2013 Western Conference finals before he and the Grizzlies parted ways. The Nets considered him last year after firing P.J. Carlesimo before hiring Kidd.
He was the only known candidate the Nets interviewed this time. King said he had reached out to one other person who chose not to pursue the job.
''If you look at (his) track record and what he did in Memphis, he was able to go in there and take a team, added some veterans and they continually got better,'' King said Tuesday. ''He developed some young guys, (Marc) Gasol, some big guys. If you look at Memphis, they got consistently got better every year. All the way to the Western Conference finals.''
Kidd led Brooklyn to a 44-38 record and the second round of the playoffs in his lone season but the Nets allowed him to pursue other jobs after denying his request for more power within the organization. The Bucks held Kidd's welcoming press conference earlier Wednesday.
Hollins is known as a strong defensive coach, with the Grizzlies holding opponents to an NBA-low 89.3 points per game in his final season. He is the franchise's career leader in wins and led them to three straight playoff appearances.
He takes over a veteran team in Brooklyn that could easily fit his style of play if Kevin Garnett and Paul Pierce return, and Brook Lopez and Deron Williams come back healthy after surgeries.
Hollins went 214-201 with the Grizzlies and improved the team's record in each of his four full seasons, from 40 wins in 2009-10 to 56-26 in his final season. Memphis upset top-seeded San Antonio in the first round of the 2011 playoffs.
But the Grizzlies came under new ownership and management during his final season, and they chose not to renew Hollins' contract after they were swept by the Spurs in the conference finals.
He met last month with Cleveland before the Cavaliers hired David Blatt.