The 25-year-old forward moved to Elland Road in January after four years with Columbus Crew in Major League Soccer.
"He can play in those creative wide areas or off the front man and adding that to our squad will only benefit us," said Stevenage manager Gary Smith.
Rogers has only started one game for Leeds and was made available for transfer last month.
Smith spent three years working in the MLS for Colorado Rapids and said on the Stevenage website: "I remember that he always did well against the Rapids and showed all of the qualities and attributes that you would want from a wide player.
"His international career reflects that, he's played against top teams at the highest level."
Rogers made his debut for the USA in 2009 and has so far won 18 caps, scoring twice.
"He's another creative option to an already growing group of players.
"The guys are knitting together and forming a very good team relationship already and I'm delighted with the speed in which that is happening," Smith added.