The items are going on display at the ground zero museum, where leaders see them as an important and moving addition to a collection that often uses personal artifacts to explore the events and impact of 9/11.
"The death of Osama bin Laden is a huge part of the history, and we have an absolute obligation to tell it," National September 11 Memorial Museum President Joe Daniels said on Saturday.
The display, he said, "allows millions of visitors the chance to recognise the extraordinary bravery of the men and women who sacrifice so much for this country at home and abroad".
The shirt and coin will join an existing display with a brick from the compound in Abbottabad, Pakistan, where the terrorist at the helm of the attacks was captured and killed.
The uniform shirt, tan with camouflage sleeves and an American flag patch - facing backward to invoke the historical role of a flag-bearer leading a charge into battle - belonged to a now-retired member of SEAL Team Six, which put an end to the long manhunt for the world's most wanted terrorist.
Police stand in front of the National September 11 Memorial Museum in New York City. (Getty Images)
The garment "connects us in a powerful and immediate way to that operation", Museum Director Alice Greenwald said.
The red, white and blue coin was made to commemorate its conclusion.
The coin bears the date - May 1, 2011, in US time - on one side and a red "X" on the other.
It was owned by the CIA officer, known as "Maya", who formed the basis for the main character in the Oscar-winning 2012 movie Zero Dark Thirty.
The museum is keeping both donors' identities secret.
