Terms of the contract have not been disclosed, but a league source told ESPNNewYork.com's Mike Mazzeo that Lopez, a restricted free agent, agreed to a four-year, $60 million max deal.
This effectively ends Brooklyn's pursuit of Howard, since Lopez can't be traded until Jan. 15 once he signs the contract, per rules of the collective bargaining agreement.
Nets general manager Billy King was in Los Angeles negotiating with Lopez's agent, Arn Tellem, on Wednesday.
"Brook Lopez is one of the top young centers in the NBA," King said. "We have witnessed his growth as a player over the past four years, and are very pleased that he will remain in a Nets uniform as we begin our new era in Brooklyn."
Lopez, 24, played just five games last season because of foot and ankle injuries, averaging 19.2 points. He owns career averages of 17.4 points and 7.5 rebounds in 251 career contests over five seasons -- all with the Nets.
The Nets finalized their other blockbuster offseason moves Wednesday, formally announcing the free-agent signings of Deron Williams and Gerald Wallace, along with the acquisition of Joe Johnson in a six-player trade with the Atlanta Hawks and Houston Rockets.
Williams, who signed a five-year deal worth $98 million, and Johnson will be introduced together Friday during a news conference at Brooklyn Borough Hall.
The Clippers will have the right to swap second-round draft picks with Brooklyn in 2016.
Teletovic averaged 16.3 points and 6.9 rebounds with Caja Laboral Vitoria of the Spanish ACB League last season.
On Thursday, Nets owner Mikhail Prokhorov released a statement saying he was "thrilled with the way our team has come together."
"My congratulations and appreciation go out to general manager Billy King, assistant general manager Bobby Marks and head coach Avery Johnson for their tenacity, nerve and heart throughout this process. With the re-signing of Deron Williams and the trade for Joe Johnson, we go into our new home led by an All-Star backcourt and with every hope of a great season for the Brooklyn Nets. I can't wait until opening night."
Mike Mazzeo is a regular contributor to ESPNNewYork.com. Information from The Associated Press was used in this report.