SEATTLE — The King County Council and the Seattle City Council gave their final approval Monday to an agreement to build a $490 million basketball and hockey arena in the city, despite the threat of a lawsuit from longshore workers.

The County Council approved it unanimously, while the City Council voted 7-2. Both bodies had previously OK’d different versions of the deal.

“This is a very good financial plan here,” said County Councilman Reagan Dunn, a Republican who earlier had concerns about the deal. “It’s been well thought-through.”

Mayor Mike McGinn called the votes important steps toward bringing professional men’s basketball back to Seattle. He and King County Executive Dow Constantine were scheduled to sign the deal Tuesday.

Hedge fund manager Chris Hansen is leading a group that wants to build the $490 million arena near the existing Mariners and Seahawks stadiums with $200 million in public financing. The public investment would be paid back with rent money and admissions taxes from the arena, and if that money falls short, Hansen would be responsible for making up the rest. Other investors include Microsoft Chief Executive Steve Ballmer and two members of the Nordstrom department store clan.

Seattle’s old NBA team, the SuperSonics, moved to Oklahoma City in 2008 and became the Thunder, devastating its fans here. It’s been quite a bit longer since Seattle had major-league hockey: The Metropolitans, who won the Stanley Cup in 1917, disbanded in 1924.

Hansen, of San Francisco, is a Seattle native, an early investor in Facebook and a big Sonics fan who approached McGinn last year about building a new arena to attract an NBA team and hopefully an NHL team as well. KeyArena, where the Sonics played, is considered outdated and financially unviable.

Under the deal, the arena proposal will undergo an environmental review that could take a year. The review will also look at whether other sites, including Seattle Center, where KeyArena is, should be considered.

But that’s not good enough, members of two International Longshore and Warehouse Union locals said Monday. The agreement between Hansen and the city goes too far by presuming the arena will be built in the neighborhood south of downtown, where increased traffic could choke freight shipments at the Port of Seattle, they said.

By essentially picking the site before an environmental review is done, the deal reverses the steps required by the State Environmental Policy Act, the unions said. They threatened to sue to block the deal once it’s signed by McGinn and Constantine.

“The cart’s been thrown before the horse here,” said Max Vekich, a member of ILWU Local 52 and co-chair of Save Our SoDo Jobs. Using a football metaphor, he added: “We want to throw a red flag here and ask for instant review.”

The unions pointed to a previous case in which Seattle approved plans for developing mixed-income housing at Fort Lawton, a former military site near Discovery Park, without providing for proper environmental review under state law. Neighbors in the Magnolia neighborhood sued, and an appeals court blocked the project.

Quoting an earlier decision, the appeals court wrote that the law’s purpose “is to provide consideration of environmental impact factors at the earliest possible stage to allow decisions to be based on complete disclosure of environmental consequences. Even if adverse environmental effects are discovered later, the inertia generated by the initial government decisions (made without environmental impact statements) may carry the project forward regardless. When government decisions may have such snowballing effect, decision-makers need to be apprised of the environmental consequences before the project picks up momentum, not after.”

But Seattle City Attorney Pete Holmes argues the agreement does not bind the city into building the arena at any particular site, and says the agreement calls for a full environmental review as demanded by state law, as well as an analysis of effects on traffic and port operations.

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