The defender was allowed to sign outside of the transfer window because he was a free agent after leaving Portuguese club Boavista in June.
"I have always wanted to play in England, this is an incredible opportunity to show what I can do," the 25-year-old said.
"I have always wanted to attack overseas football because I think that is where the best players are, and that is how you find your better game and develop, so I really think this will help me achieve the best that I can be as a footballer."
Cannon previously played for FC Dallas and joined Boavista in 2020.
QPR plays in the English second division and was last in the Premier League in the 2014-15 season.
The club said the transfer was subject to approval by FIFA, the FA and English Football League. Cannon will also need to receive international clearance.
"We have fought off clubs to get him and I believe Reggie will become a big asset for us," QPR head coach Gareth Ainsworth said.
"He can play on the right side of midfield as a wing-back, he can play as a right-sided centre-back, so he is going to add real competition for places which is what we need.
"With him being without a club over the summer he is going to need a bit of time to get up to speed but I know he is raring to get going with us."
Cannon has made 28 appearances for the U.S., scoring one goal, and last featured in a September 2022 friendly against Japan.
The Associated Press contributed to this report.