The museum includes two core exhibitions at the foundation of the trade center complex.
One of them, called "In Memoriam," pays tribute to the 2,983 people killed in the Sept. 11, 2001, attacks as well as the six people killed in a truck bombing at the trade center on February 26, 1993. The other, a three-part historical exhibition, tells the story of Sept. 11 and explores what led to the terrorist strikes.
The museum's regular hours will be 9 a.m. to 8 p.m. daily.
"This is a major milestone," Daniels said. "It's just a very real marker of the rebirth of the World Trade Center."
Planners had originally hoped that the museum could open in 2011, on the 10th anniversary of the attacks. Construction delays were made worse by flooding caused by Superstorm Sandy and by a funding dispute with the site's owner, the Port Authority of New York and New Jersey, stopping all work for nearly a year.
The planned ticket price of $24 has angered some Sept. 11 family members.
Retired Deputy Fire Chief Jim Riches and Sally Regenhard, each of whom lost firefighter sons in the attacks, complained earlier this year that the museum "was never intended to be a revenue-generating tourist attraction with a prohibitive budget and entrance fee." Museum officials defend the planned ticket price, saying the museum's operations are privately funded.
Daniels said there will be no admission charge for relatives of Sept. 11 victims or for rescue and recovery workers. Children age 6 and younger will get in free, and admission will be free for everyone on Tuesdays from 5 p.m. and 8 p.m.
There will continue to be no charge to enter the World Trade Center memorial plaza, which is already open. About 5.3 million people visited the plaza last year to see the two huge fountains that sit in the original footprints of the twin towers.