Hollins' deal could be worth as much as 4 years, $20 million if the team picks up his fourth-year option, a source told ESPN.com's Ramona Shelburne.
"We have a nice nucleus to build with," Hollins told Shelburne. "We want to be better than last year, and obviously that's going to take work. We're going to work hard, be aggressive and we're never going to quit."
Hollins led the Memphis Grizzlies to three consecutive playoff appearances in his last three seasons with the team. In 2012-13, his final year at the helm, the Grizzlies won 56 games and advanced all the way to the Western Conference finals. The two sides ultimately decided to part ways, and Hollins' contract was not renewed, apparently because there were philosophical differences between him and ownership.
Hollins takes over for Jason Kidd, who left the team for the Milwaukee Bucks earlier this week.
Sources say the Nets wanted to move quickly in the wake of the Kidd saga and focused on Hollins immediately, meeting with him Monday and Tuesday.
Hollins has been a favorite of Nets officials for some time and was pursued by Brooklyn to serve as an assistant to Kidd after the in-season departure of Lawrence Frank, but the former Grizzlies coach was determined to wait for a head-coaching opportunity. Hollins was also chased hard this spring by the Houston Rockets to serve as the top aide to Rockets coach Kevin McHale in the event that Hollins didn't land a top position.
"I'm humbled," Hollins said. "The process to get back in the league was a long one. But I'm thankful to God because I believe this is the perfect fit for me."
Nets general manager Billy King, during an appearance Wednesday on ESPN Radio's "Mike & Mike," said experience would be key when making the team's next head-coaching hire.
"One, I think we're looking for experience, someone we'll build with for a long time," King said. "Someone who can develop young players, develop veterans and have a tough mindset. But someone also who has the experience who can take us to where we want to go."
On Tuesday, King praised Hollins' work in Memphis.
"If you look at his track record and what he did in Memphis, they consistently got better every year," he said.
Hollins said his first order of business is to meet with players including Kevin Garnett, Deron Williams, Joe Johnson and Brook Lopez. He also said he'd help King in any way he can with free agents such as Paul Pierce, but will follow King's lead.
The deal with Hollins caps a tumultuous week for the Nets.
King learned of Kidd's intentions to leave for Milwaukee last Wednesday. After completing his rookie season as Nets coach, Kidd went to ownership and asked for final say in player personnel decisions, King confirmed during an interview on ESPN Radio on Wednesday.
The Nets said no and Kidd's agent, Jeff Schwartz, asked for permission to speak with the Bucks.
The teams eventually decided on compensation for Kidd, with the Bucks trading two second-round draft picks (2015, '19) for him in a deal that became official Tuesday.
ESPN.com's Ramona Shelburne contributed to this report.