Trimble averaged 15.9 points, 3.7 rebounds and 3.9 assists a game in three years with the Maryland Terrapins. He was also a 34.3 percent shooter from beyond the arc.
The 22-year-old also made three appearances for the Philadelphia 76ers in the Las Vegas Summer League, averaging 10.3 points.
"In the position I'm in, not being drafted and trying to make a team and all that, I'm not going to be the first or second option," he said. "I might not be an option at all. But I'm going to do my role, and these next couple years for me is just getting where I fit in."
Jeff Teague signed a three-year, $57 million deal with the Timberwolves this summer, and third-year guard Tyus Jones will back him up at the point.
Breaking into Minnesota's rotation won't be easy for Trimble. He'd likely benefit from spending most of his rookie year with the Timberwolves' NBA G League affiliate, the Iowa Wolves, where he can gain professional experience and possibly prove himself worthy of an NBA roster spot in Minnesota or elsewhere.