The fixture on 15 November will be the last at the National Stadium before it is closed for redevelopment ahead of the Commonwealth Games, which are being staged in Glasgow next summer.
The match gives the Dark Blues the chance to gain revenge for the 5-1 mauling handed to them by Jurgen Klinsmann's side in Jacksonville, Florida, last year.
Former boss Craig Levin was in charge for that humiliating display but this fresh test will be a chance for current boss Gordon Strachan to shape his side ahead of the UEFA Euro 2016 qualifying campaign.
Scotland have already seen their hopes of qualifying for next year's World Cup in Brazil dashed, but the US have already booked their place at next summer's showcase.
Strachan said: "I am looking forward to playing the USA at Hampden Park in November. While it would be great to be preparing for the World Cup in Brazil, or taking part in the play-offs, this match will give us another opportunity to maintain the momentum achieved with the results and performances against Croatia and Macedonia.
"I have been greatly encouraged by the improvement shown by the squad in recent months and by the unwavering support of our excellent fans. I am sure both the players and the Scotland supporters will look forward to the opportunity to finish the year positively."
Klinsmann added: "The game against Scotland is crucial for us because we have so few games between now and when we name the roster for the FIFA World Cup.
"It's a huge opportunity for the players, and we are excited to play against a team and in a venue that has so much tradition and history in football."
The SFA also hopes to announce plans for an away friendly - scheduled for Tuesday, November 19 - in due course.