Hochtief's Turner subsidiary is to manage a "full-scale transformation" of the iconic New York arena used for basketball, ice hockey, big boxing bouts, political conventions, concerts and other events, a statement said.
No amount was given but industry sources have said the work, due to take place during three consecutive summer periods, would cost around $775 million (€601 million).
Turner built the original structure in 1968, and will now create "a new entrance and wider concourses with views of the city," the statement said.
A major new element will be two bridges that measure 61 metres (yards) in length and span the space, providing fans with a view from 21 meters above the playing surface.
Sight lines inside the cavernous arena are also to be improved and more comfortable seating installed, while lower level suites are to be enlarged and moved closer to the action.
A new scoreboard, state-of-the-art lighting and LED video systems are also in the works, along with renovated food areas and television broadcasting sites. Turner will also restore the Garden's distinctive domed ceiling, Hochtief said.
According to the New York Times, the arena will be shut down each year after the New York Knicks basketball team and the Rangers ice hockey team close out their seasons.
Work is to begin in 2011 and be completed in 2013.