Gladbach was relegated at the end of last season and did not re-sign Keller, who played for the USA this summer at the Gold Cup and Copa America, upping his cap total to 102.
At Fulham he joined fellow Americans Clint Dempsey, Carlos Bocanegra and Brian McBride.
Keller's acquisition by Fulham was spurred by an injury to starting keeper Antti Niemi.
"I'm delighted that Kasey has joined us, and I'm sure he'll be a great addition to the squad," said Fulham coach Lawrie Sanchez. "Obviously, with Antti being injured, it was important we added some strength and depth in that area, and Kasey is a proven professional with impeccable international credentials
"It's vital we have cover in all areas throughout the squad, and I think he will be a valuable asset to us over the course of the season."
Keller says he is delighted at the opportunity to show what he can do again at the top level in English football.
"It's fantastic to be back in the Premier League after a couple of years' absence," Keller said.