"This shirt is a symbol of the bravery of the US Navy SEAL Team 6, who risked their lives," Congresswoman Carolyn Maloney, who brokered the effort to secure the artifact, was quoted as saying by the New York Post.
The shirt, worn by the Navy SEAL during the night time raid in which he shot bin Laden to death in 2011 in the garrison town of Abbottabad, will be put on public display at the 9/11 Memorial Museum starting Sunday.
His identity has never been revealed because of concerns for his safety - and his name will not be included in the display of the shirt, which is brown with a black American flag on the sleeve.
The now retired Navy special-ops soldier is so concerned about being exposed that he cancelled a meeting with the families of 9/11 victims out of concern for preserving his anonymity.
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In fact, the shirt will only be ID'd as a shirt belonging to a member of the SEAL team that took out bin Laden, though the daily quoted sources as saying that it was worn by the actual shooter.
"It's important that they tell the entire story, not just the story of the 9/11 attacks," she said.
Little is known about the SEAL who gunned down bin Laden.
In a 2013 interview with Esquire magazine, the SEAL remembered the fear that he felt before embarking on the mission and recalled writing what could have been his last letter to his family.
After he came home, his life has been a struggle. He has had trouble finding work and his wife separated from him.