The suit had been out of view and needed to be restored before it was put on display at the Air and Space Museum in Washington.
On hand for the unveiling were vice president Mike Pence, NASA chief Jim Bridenstine and Mr Armstrong’s son Rick. A fundraising campaign took just five days to raise the $500,000 (£400,000) needed for the restoration.
Calling Mr Armstrong a hero, Mr Pence said “the American people express their gratitude by preserving this symbol of courage”.
The Apollo 11 crew of Mr Armstrong, Buzz Aldrin and Michael Collins launched to the moon 50 years ago on Tuesday.
Mr Armstrong died in 2012.