The 23-year-old, who moves to Ibrox for an undisclosed fee, has put pen to paper on a four-year-contract.
"I'm very pleased," McCoist told RangersTV. "David has always been our number one target and we're delighted to sign him up.
"I was always confident that we would have a good chance of signing him and judging by one or two of the comments in the newspapers from him I felt we had a chance.
"It's particularly pleasing because he is coming off a couple of great performances and you could say results against one of the top sides in the English Premier League."
After joining Hearts from Stenhousemuirfor for a fee of £30k in January 2007, Templeton scored 11 goals in 80 SPL matches.