Peters, a graduate transfer, is a former Mr. Football in Indiana who played 10 games with four starts at Michigan, passing for 680 yards and four touchdowns. He completed 58 of 110 passes in his first two seasons, including a career-high 20 completions for 186 yards in the Outback Bowl against South Carolina in January 2018.
"We loved Brandon when we got a chance to know him during the recruiting process," Smith said. "Now that we've seen him on the field, he has been everything we though he would be. He has really thrown the ball well and is a better runner than he's given credit for. Most importantly, he has moved into a leadership role for us."
Peters transferred to Illinois this summer with two years of eligibility remaining.
Illinois opens the season at home against Akron on Aug. 31.