But Edward P. Mangano, the Republican county executive, blamed his rivals for blocking his efforts to overhaul the Nassau Coliseum and the 77-acre Nassau County Hub that surrounds it. “No one has done more to retain the New York Islanders than my administration,” he wrote on Twitter. “It’s sad and unfortunate that political opponents chose to oppose my plan and instead continued to support the Culture of NO on Long Island.”

It is unclear what effect the arrival of the Islanders might have on the Rangers, with their fiercely loyal fan base, or the New Jersey Devils, who play in Newark. Both teams had supported the idea of a new Islanders arena on Long Island.

The Rangers are owned by Madison Square Garden, which broadcasts the Islanders’ games. And the Rangers are in the midst of a three-year renovation of the Garden and have been steadily raising ticket prices. So any extra income would probably offset any loss of fans who might, for whatever reason, switch allegiances (just as some Knicks fans have threatened to support the Nets after the team declined to re-sign Jeremy Lin).

The Barclays Center is not ideally suited for hockey — a hockey rink is bigger than a basketball court — and the size of the arena’s interior was reduced to pare costs. As a result, the arena has room for 14,500 seats for hockey, far smaller than most other hockey stadiums and 3,500 seats fewer than are available for Nets games. The Islanders’ current home, the Nassau Veterans Memorial Coliseum in Uniondale, has a capacity of about 16,250, but the team’s average home attendance last season was 13,191.

Still, the team’s move to Brooklyn leaves many unanswered questions, especially for a contingent of steadfast opponents of the development project — which includes a plan for 15 residential towers over the next 25 years and possibly an office building or hotel — who view it as a publicly subsidized land grab that featured a string of broken promises and threatens to overwhelm the adjacent neighborhoods.

“My longtime concerns with the Barclays Arena and Atlantic Yards project continue to remain — living wage jobs, affordable housing and quality of life,” said Councilwoman Letitia James of central Brooklyn. “I look forward to reviewing this deal with my colleagues.”

Current Islanders season-ticket holders will have first rights to buy tickets in Brooklyn. Within minutes of the announcement, Barclays was selling them.