According to Callis, Stewart and the Tigers agreed on a $1,795,100 signing bonus, the full slot value for the No. 35 overall pick.
Burrows tweeted, "I'm officially a Detroit Tiger," on Tuesday morning.
The club has not confirmed either deal.
Stewart, out of Tennessee, hit .311 in 50 games for the Volunteers this year. He hit 15 homers and drove in 47 runs.
Burrows, a righty out of Weatherford High School in Texas, was a 2015 Perfect Game 1st Team All-America.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak.