Urquhart has put pen to paper on a three-year deal after the Sky Blues agreed a compensation package for the centre-half with the Scottish club.
The 18-year-old was out of contract at Ibrox but because Rangers had offered him a new deal in the summer, Coventry had to pay compensation.
"We are absolutely delighted to get Stuart," said Sky Blues boss Steven Pressley.
"He's a player I've had my eye on for some time and I believe he has a great future ahead of him.
"Stuart will come into our under-21 development squad set-up but, as we have shown this season, the path to the first team is there for every player - no matter how old they are - if they work hard and impress."