The film, which includes "4-D" elements such as props and shaking seats, opens to the public on Friday and will be shown exclusively at the museum's new Victory Theater.
The theatre is part of the museum's $300 million (£180.65 million) expansion project that will continue through 2015.
Clarkson and Cromwell were among more than a dozen celebrities who lent their voices to the documentary.
Clarkson as the voice of Marguerite Higgins, a New York Herald Tribune correspondent, and Cromwell as the voices of Maj Gen Alexander Archer Vandegrift and Fleet Adm William Halsey.
The film includes vintage images that chronicle WWII - from Pearl Harbour to the Battle of the Bulge - and took five years to make.
"I'm just glad that it's here," Hanks said. "I'm glad that it's part of the bigger museum. I think things like this are natural resources for each city (in which) they exist."
Hanks said the film also captures a moment in the country's history that "is now entering into the era of myth".
He noted that younger generations are far removed from World War II and hopes the film will bridge the gap.
"It was all heroes long ago," he said, but notes that there's still much to learn from history.