The new deal will keep McKay at Ibrox until May 2018.
McKay told the club’s official website: “It means a lot and it shows everyone how far I’ve come in the past year to earn myself a new deal which I am happy to sign.
“I was there when the journey back started and hopefully now we are going to finish it, and seeing it through will be a great personal achievement.
“I made my debut when I was 17 and the change in me from then to now has been massive, and I feel the manager and Davie have given me a lot of confidence this season.
“They have been great with me and I have a lot to thank them for.”
The pacey winger has made 78 appearances for Rangers since making his debut in July 2012 against Brechin City.