Gov. Andrew Cuomo (D-N.Y.) tweeted pictures of what the planned makeover will look like, saying, "It's going to be a lovely front door to NY".
Delta's $3.4-billion investment into the terminal construction on the eastern part of the Queens airport is the largest in the airline's history.
It's going to be a handsome front door to NY.
Delta and its partners will pay $3.6 billion for the new facility, with the Port Authority of NY and New Jersey providing the remaining funding.
"Today's groundbreaking at Delta's facilities represents another step forward as we build an entirely new airport at LaGuardia", Cuomo tweeted.
"LaGuardia is a pillar of New York's transportation network and a key driver of economic growth, but for too long the airport has been unworthy of New York State", Gov. Andrew Cuomo said at the Delta groundbreaking ceremony.
The first gates at the new facility are expected to open next year.
The new Delta facilities come in addition to a separate $4 billion public-private partnership that is already underway to rebuild the airport's central terminal and move it closer to the Grand Central Parkway.
Delta announced in late July it would directly fund and finance the costs of its LaGuardia Airport redevelopment project, which would renovate Delta's terminal.