The contract will probably keep the 35-year-old at the club for the rest of his career.
“We are delighted we have been able to extend Frank’s contract early,” said HSV sports director Dietmar Beiersdorfer.
“He is not only a strong foundation to our team, but he has developed a strong identity with the city and the club while he has been here.
“Therefore, he will remain with HSV in a sporting capacity after he ends his playing career.”
Rost joined Hamburger SV from Schalke in 2006.