Known as the New Jersey Nets for 35 years, the team will start the new season in the famous New York borough, and in a new stadium, the Barclays Center.
Jay-Z, who owns shares in the club, has been a prime mover behind the NBA team's reincarnation, advising club executives, as well as designing club logos and apparel.
He also stars in a series of eight sold-out concerts, starting on Friday, 28 September, to open the multi-purpose venue, which will be used for everything from sporting events, to concerts, to family shows.
The music star, real name Shawn Corey Carter, was brought into the Nets fold in the mid-2000s by then-owner, and current minority stakeholder, property developer Bruce Ratner.
It was Mr Ratner who also came up with the idea of moving the team to sports-mad Brooklyn, without a major professional sports team since the Brooklyn Dodgers baseball team moved to Los Angeles in 1957.
Ownership 'vision'
"When Bruce Ratner first bought the team he brought Jay-Z into the ownership structure - that showed foresight," says Brett Yormark, Brooklyn Nets chief executive.
"Jay-Z is from Brooklyn, he is of Brooklyn. So he recognised the vision when Bruce first announced his intention to come to Brooklyn."
Mr Yormark says: "Jay-Z's role with the team has evolved." And the rapper worked closely with club executives on the two new club logos - one with a shield and one with a large B - and colours.
"He is a confidant that I can reach out to - he has a tremendous understanding of current consumer trends," the Mr Yormark, 45, adds.
The move completes a near eight-year battle for Mr Yormark to get the team into its new $1bn (Â£0.6bn) home, having to overcome the global financial crisis on the way.
"We are very excited - I honestly think the Barclays Center, and the move of the Nets, has exceeded people's expectations," he says.
"It has taken time to get to Brooklyn, but on 30 April we turned the page."
That was when the red, white and blue of the New Jersey Nets was exchanged for the black and white Brooklyn look.
The Brooklyn borough is roughly 10 miles (16km) across the Hudson from Newark, New Jersey, last home of the Nets.
"It has been an incredible time since April - the public has really connected with the 'Brooklyn-isation' of our offer," Mr Yormark says.
If its population was counted separately from that of New York, then Brooklyn would be the fourth biggest city in the US, offering a large potential fan-base.
Mr Yormark says that sales of merchandise are going very well, and doing better than some long-established teams.
Demand has exceeded expectation, and Mr Yormark was also pleased to see club merchandise on sale in London during a recent visit, given that the Nets are looking to create a global fan-base.
Like all NBA teams, China is a major potential market, but for the Nets there is another specific nation they are targeting, the homeland of club majority owner Mikhail Prokhorov.
"We have an eye on Russia - that is a market we are keenly interested in," says Mr Yormark.
"Our goal is to be the home NBA team in Russia."
And whereas the club previously sold 4,000 "full season seats", during their time in New Jersey, they have sold more than 10,000 of these season tickets for the 18,000 capacity Barclays Center.
There is a wide range of tickets, to suit all incomes. At the top end there are 1,200 executive suite seats, and at the other there are 2,000 tickets available at $15.
"It is part of our message to the community - we want to make sure that anyone can attend a game," says Mr Yormark.
The Barclays Center will also provide 2,000 jobs for local people.
There are also Nets ticket packages, which call for a commitment of three years, but which allow access to tickets for other events at the Barclays Center before the general public can buy.
"This was the first product of its kind in New York," says Mr Yormark.
"If you are a business person and you know you are going to need tickets for college sport, boxing, family shows, then you know you can get them from the Nets."
He says that some 12% of the ticket base that was with the Nets in New Jersey has pledged to follow the team over in Brooklyn.
"We try to do our best for fans," says Mr Yormark. "We promised that if they stuck with us [for the last season] in New Jersey they would get first chance at the Brooklyn tickets."
Meanwhile he says that sponsorship income is up three times on last year's figure.
Barclays is the title sponsor of the new venue, and there are 12 founding partners, which include big names like American Express and Honda.
"It is an exciting time - you don't often get a chance to transfer a team into a new major market."
The move will certainly establish a local rivalry with the New York Knicks team, who the Brooklyn Nets will play in the first match of the season on 1 November.
"The first game will make for a very tremendous moment, and gives people a lot to talk about," says Mr Yormark.
The move has not been without its difficulties, with protests and political hurdles to be overcome.
But Mr Yormark sees the delays as actually having had a beneficial effect.
"I look at everything with a silver lining," he says.
"The economy is better than it was, Brooklyn is a more dynamic market than it was, the time is right to bring sport back to Brooklyn."
Few, if any, leading sports clubs can say that a top rap star has played a role in their rebirth, but that is the case with the newly founded Brooklyn Nets basketball team.