King joined Rangers on loan from Scottish Premiership side Heart of Midlothian in the January transfer window.
Sbragia, who is currently the head coach of the Scotland Under-21 national football team, believes that the 21-year-old winger will be a success at Ibrox.
"Rangers are getting someone they know can play championship football week in, week out,” Sbragia told Herald Scotland about King. “Someone who has played at places like Alloa before, dealt with the artificial surface, and generally been part of a successful championship campaign.
“Learning how to handle playing in front of 50,000 each week at Ibrox will be great for his development. But from his point of view the main thing is that he will be looking to play football. The bottom line is you've got to be playing.”
Sbragia made the comments about King before the game between Rangers and Falkirk at Ibrox in Glasgow at the weekend.
King did not start the Scottish Championship match, but he proved to be the difference between the two sides on Saturday afternoon. The 21-year-old winger came on as a substitute on the hour mark and scored the winner in injury time.
Rangers are at the top of the Scottish Championship table at the moment with 56 points from 22 matches. The Glasgow giants are eight points clear of second-placed Hibernian, who have a game in hand.
Mark Warburton’s side will return to league action this evening when they take on Raith Rovers away from home at Stark's Park.