Robertson started six games and also spent time in the bullpen for the Tigers last season. He finished 2-3 with a 5.44 ERA in 28 appearances.
The trade enables Robertson to start with the Marlins and assures left-hander Dontrelle Willis a spot in the Detroit rotation.
"I think it's a great situation for Nate. I assume he's going to be a starting pitcher there, which is what he wants to be," Detroit manager Jim Leyland said in Sarasota after the Tigers beat the Baltimore Orioles 10-9.
"He's been nothing but a good soldier here over the years. We appreciate everything he's done for us," Leyland said of Robertson. "I think this is a great opportunity for him and it unclogs the issue for us a little bit."
Leyland said Willis would take the No. 3 spot in the rotation. He figured Robertson did not want to be a reliever in Detroit.
"He probably would have not been a happy camper if it would have worked out that he was in the bullpen," Leyland said.
Owed $10 million this year in the final season of a $21.25 million, three-year deal, Robertson has a 51-69 record and 4.92 ERA in 202 games over eight big league seasons. Detroit is sending Florida cash as part of the deal.
The 22-year-old Voss split last season between Class-A Jupiter and Double-A Jacksonville for the Marlins. In 10 games with Jupiter, he compiled a 2.03 ERA and 10 strikeouts. He was 3-0 with a 2.97 ERA and 36 strikeouts in 30 appearances with Jacksonville.