The 23-year-old seamer has impressed in the second XI as joint leading wicket-taker across all formats with 29 competitive wickets and scored an unbeaten half-century with the bat.
The seamer, who can bats at lower-order lineup, has also scored a century and seven 50s this season.
He said: “I’ve really enjoyed my time at Kent and I’m delighted to get the opportunity to work with the first-team squad and coaches.
“Becoming a full-time professional means I can dedicate more time to developing my game and I hope I can contribute to some success for the club.”
Stewart is not considered as an overseas player as the all-rounder has an EU passport through his mother’s Italian ancestry.