According to ESPN.com's Adam Schefter, Detroit sent the Rams a 2018 sixth-round selection in return for Robinson.
Robinson was the No. 2 overall pick in 2014 out of Auburn and was expected to start at left tackle.
"Since we drafted Greg, he has been committed to our organization, his teammates and community outreach," Rams general manager Les Snead said in a statement. "We appreciate his dedication and the effort he's put forth over the past three seasons. We wish him the best as he embarks on this new chapter."
Robinson struggled in that role and the team declined his fifth-year option last month, making him a free agent at the end of this upcoming season.
The Lions are trying to fill a spot after Taylor Decker injured his shoulder, sidelining him through at least training camp.
In 2016, Robinson started 14 games at left tackle and had started 40 games for the Rams during his time with the team.