Kuss becomes the first American to win a Grand Tour since Chris Horner did so ten years ago.
His Jumba-Visma team finished first, with Tour de France winner Jonas Vingegaard second and Giro d’Italia winner Primoz Roglic third.
Groves sped to the final stage victory, just holding off the pack.
It was the third stage victory for the Australian. He was part of a six-man breakout and made the critical move with 37 kilometers remaining on a 100-kilometer stage that included 20 loops around Madrid.
The peloton closed up on the escape in the final metres, but Groves, who won the overall sprinter’s jersey, crossed first, ahead of Italy’s Filippo Ganna and Germany’s Nico Denz.
Kuss and his teammates stayed out of trouble and finished the stage together to become the first team to complete a clean sweep of this season’s Grand Tours.