The Federal Transit Administration has released the first $100 million installment of the total approved $1 billion in federal funding for the Massachusetts Bay Transportation Authority’s 4.7-mile light rail line extension from Cambridge to Medford, two inner-ring Greater Boston communities.

FTA officials notified the MBTA’s Green Line extension project team on Thursday. With federal funding in place, the MBTA, which operates mass transit in Greater Boston and which locals call the “T,” issued a notice to proceed to the design-build team, GLX Constructors.

After a sealed-price opening last month, GLX Constructors won with its bid, a total of $1.08 billion. GLX Constructors consists of Fluor Enterprises Inc., Middlesex Corp., Herzog Contracting Corp. and Balfour Beatty Infrastructure Inc.

Cost overruns forced Massachusetts to put the project on hold two years. The commonwealth, however, must finish the project because Washington ordered it as part of traffic mitigation for the $24.3 billion megaproject known commonly as the Big Dig. The new target date for the Green Line extension is December 2021.

“This has been a long haul but we are where we need to be with today’s news,” said state transportation Secretary Stephanie Pollack.

The MBTA, a unit of the state Department of Transportation, has answered to a state-run Fiscal Control and Management Board, created after Boston’s snow crisis in 2015.

“To system users whose train or bus was late today, the claim that the T is already undergoing a turnaround may seem a stretch,” the oversight board said in its third annual report, issued Dec. 15. “However, comparing the state of the system when this board was created less than three years ago to its state today shows a clear arc of progress.”

The T whittled its deficit for fiscal 2017 to $30 million from a projected $242 million, with savings from operating costs going directly to system improvements.

Necessary improvements, said the oversight board, include management of operating and capital budgets; improving on-time performance, notably for buses; controlling pension costs; and streamlining procurements.

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