California-born Steel, 21, has played for the first team in all three competitions this season.
He made his maiden first-class century last month, scoring 128 against Northamptonshire at the Riverside.
"He's demonstrated real talent this year and contributed well in both the red and white ball format," coach Jon Lewis told the club website.
"His continuous improvement with the bat has been extremely pleasing and we're keen to develop his role as a leg-spinning all-rounder."
Durham batsman Cameron Steel has extended his contract with the club until the end of the 2019 season.