The 28-year-old had been without a club following his release by Bristol Rovers at the end of last season.
"We are delighted to get him signed up," Dundee boss Paul Hartley told the club's official website. "He hasn't really played as a main striker for a few years but we see him as a centre forward. He will give us good competition."
Clarkson began his career with Motherwell in 2002 before spells with Bristol City, Brentford and Bristol Rovers.