"This marks the true beginning," said Gretchen Dykstra, president of the World Trade Center Memorial Foundation.
"After September 11, many people around the world built temporary memorials and now it is time to build a permanent memorial to pay tribute to those who died and to bring understanding to future generations," Ms Dykstra said.
The design, "Reflecting Absence" by architect Michael Arad, was chosen from 5,201 entries submitted to an international memorial competition.
The main feature will be two reflecting pools, surrounded by gardens, in the footprints of the fallen twin towers.
The pools will be almost empty, with water running down the sides to symbolise the vacuum left by the 2,749 people who died when two hijacked planes were crashed into the trade center.
Some of the victims' families are unhappy with the plans to incorporate the footprints, which they would prefer to see preserved intact.
Last week, the Coalition of 9/11 Families filed a lawsuit in New York seeking an injunction to halt the construction work. Arguments will be heard in court on Wednesday.
Coalition executive director Anthony Gardner said the footprints were irreplaceable. "They are the last scar that 9/11 has made on this soil," Mr Gardner said.
"One hundred years from now, they'll resonate more with visitors than any memorial or any museum we build on that site," he added.
New York Mayor Michael Bloomberg said he was opposed to any further delay in the memorial project, which has struggled to achieve a consensus ever since its inception.
"I think the time for expressing yourself has come and gone. And now we should rally behind this design and go ahead and support this memorial," Mayor Bloomberg said.