Charania added the agreement is for two years and $8.3 million with a team option.
Robinson spent each of the past three seasons with the Indiana Pacers before hitting the open market.
Last season, Robinson appeared in 23 games and averaged 4.1 points and 1.6 rebounds, while shooting 42.4 percent from the field and a career-best 41.2 percent from three-point range.
The Gary, Indiana, native's best NBA season came in 2016-17 when he appeared in 69 games and made 27 starts.
Robinson averaged 6.1 points and 3.6 rebounds per contest, and he shot 46.7 percent from the floor and 39.2 percent from deep.
He was originally selected by the Minnesota Timberwolves in the second round of the 2014 NBA draft after two productive collegiate seasons at Michigan.
Robinson was claimed off waivers by the Philadelphia 76ers during his rookie campaign, and he then signed with the Pacers during the ensuing offseason.
The 24-year-old Robinson is the son of Glenn Robinson, who spent 11 seasons in the NBA (primarily with the Milwaukee Bucks), and was a two-time All-Star.
Robinson III's most notable NBA accomplishment came in 2017 when he won the Slam Dunk Contest.
Although his production has been somewhat limited, Robinson is a strong addition for Detroit on the surface.
He can play both small forward and shooting guard, and he will join a rotation that already includes Stanley Johnson, Luke Kennard and Reggie Bullock.
Robinson has shown in a fairly small sample size that he is a quality three-point shooter, and that should be a fine complement to Detroit's frontcourt duo of Blake Griffin and Andre Drummond.