
After a state-wide manual recount Mr Franken was declared the winner, but Mr Coleman fought the result in court.
The Supreme Court ruling means that Mr Franken should soon become the Democrats' 60th vote in the US Senate.
Sixty votes are needed to overturn attempts by the Senate minority to block legislation using a technique known as a filibuster.
Mr Coleman has not publicly ruled out continuing his fight in the federal courts.
In earlier court hearings, his legal team complained that a number of absentee ballots had been unfairly rejected by local officials.
But the Minnesota Supreme Court rejected Mr Coleman's arguments.