"There is no doubt that it will be done by next spring in advance of the next anniversary," said Joe Daniels, president of the September 11th Memorial and Museum foundation.
The complex nature of the construction, which is taking place underground, has made for slow going, and there has been a dispute over financing with the Port Authority that CBS News said brought work to a halt for months last year.
The museum entrance includes massive steel girders from the World Trade Center as well as part of the staircase WTC workers used to evacuate one of the doomed towers.
Some of the museum exhibits, including rescue vehicles that were wrecked in the collapse, are already in place.
"I'd put us in the 75 percent-there stage, although this last 25 percent is some of the most difficult work, which is the installation of the exhibitory itself," Daniels said.
2014: The Year in Music [PHOTOS]