Koller has decided to leave Borussia Dortmund for Monaco after four seasons in Germany.
The 33-year-old arrives in The Principality on a free transfer after seeing out his contract at Dortmund.
The giant striker endured an injury-ravaged season last term after picking up a serious knee ligament problem.
Koller has regained his fitness and is set to lead his country's attack at this month's World Cup finals.
Koller has agreed a two-year deal at Stade Louis II and Monaco will hope he can help improve on their disappointing campaign last term.