Hensley, 18, was the 30th overall selection and recently graduated from Santa Fe High School in Edmond, Okla., where he was named the 2012 Gatorade Oklahoma "Baseball Player of the Year."
Hensley's deal is worth $1.2 million, slightly below the recommended slot bonus of $1.6 million. A routine MRI exam last month revealed an abnormality in Hensley's pitching shoulder, but he has experienced no symptoms or pain and continues to throw with his full velocity.
"I'm excited that I get to join such a prestigious organization with so much history and tradition," Hensley said. "I'm lucky to have this opportunity, and I'm looking forward to getting my professional career going and getting to the big leagues as quickly as possible."
The Yankees had until Friday's 5 p.m. ET deadline to complete the deal. Hensley had committed to the University of Mississippi before being selected by the Yankees.
Hensley has been said to top out around 94 mph with his fastball and owns a 12-to-6 power curveball that the right-hander says is his best pitch. He also continues to hone a developing changeup.
Hensley went 10-0 with a 1.52 ERA in 11 games as a senior in 2012, striking out 111 batters in 55 1/3 innings.
Listed at 6-foot-4 and 220 pounds, Hensley became just the seventh Oklahoma pitcher to be selected in the first round out of high school.
Hensley's father, Mike, was a second-round pick in the 1988 Draft and played in the St. Louis Cardinals' Minor League system from 1988-90 before beginning a coaching career at Kansas State University.