Backers of the proposed Southwest light-rail line were nearly giddy Thursday after announcing that the federal government had granted the controversial $1.84 billion project a green light that moves it closer to construction.

“We’re not breaking out the champagne yet, but this is still outstanding news,” said Adam Duininck, chairman of the Metropolitan Council, the builder and ultimate operator of the 14.5-mile line slated to link downtown Minneapolis with Eden Prairie.

The announcement, considered a key milestone in transit planning, was made at a Southwest Corridor Management Committee meeting, an advisory group.

The Federal Transit Administration (FTA) notified the Met Council last Friday that it had granted the project a “record of decision,” meaning environmental work has been completed on the line.

Such a decision is typically followed by the engineering phase, when bids are let for construction of track, stations and other infrastructure.

There’s still the not-so-small matter of the missing $135 million in local funding — money that was supposed to come from state coffers.

Lawmakers, deeply divided along party lines, put the kibosh on the final 10 percent piece last spring, threatening the line’s future and leaving Southwest planners scrambling to find another funding source. Local funding must be shored up before the FTA kicks in its share, about $919 million.

Duininck said he was pleased that Gov. Mark Dayton is working toward calling a special session of the Legislature for August.

While he doesn’t expect Southwest funding to be part of any deal in that session, he said, there may be some wiggle room that could open doors for money to come from other sources.

Those sources likely would include Hennepin County, where the entire line would run, and the Counties Transit Improvement Board (CTIB), which collects a quarter-cent sales tax for transit in five metro counties.

CTIB is already on the hook for 30 percent of the project’s capital costs, and the Hennepin County Regional Railroad Authority for 10 percent.

“If there’s a way that we can solve this on our own, we should do it,” Duininck said. “The challenge is that there’s always way, way better options that include the Legislature’s actions.”

Although the FTA considers the environmental work complete, a lawsuit challenging the project on environmental grounds is pending in federal court. The Lakes and Park Alliance, a Minneapolis group, claims the project violates federal environmental laws.

The price tag of the project has risen from $1.79 billion to $1.84 billion. Actual costs haven’t increased — the new price includes $69 million in land values from parcels donated to the project by Hennepin County and the cities of St. Louis Park, Hopkins, Minnetonka and Eden Prairie.

Previous estimates put the value of that land at $30 million, but appraisals came in higher. That means the FTA’s expected 50 percent match would increase by $24 million.

Because environmental work took longer than expected, the line now is expected to begin service in 2021 — the same year as its sister project, the Bottineau Blue Line light-rail project in the northern suburbs.