The 19-year-old was one of new Cappielow chief Kenny Shiels' first signings when he replaced Allan Moore as boss, with the Gers kid agreeing a short-term deal last month.
The Ton's abandoned Championship clash with Queen of the South on Saturday was due to be his final match for Shiels' side.
But after holding talks with the Light Blues, Shiels has now struck a deal to keep McKay at Cappielow until the end of the campaign.
The capture of McKay is a major boost to the Ton as they bid to haul themselves away from the Championship relegation zone, with the Murray Park kid now set to benefit from an extended period of first-team football.
Shiels told SportTimes: "Barrie is coming back to us until the end of the season. It has been agreed. We'll do the paperwork and that will be it.
"He has made a good impact for us since joining us so it is great news for us.
"He is a good player so we are pleased to have him until the end of the season.
"It is good for us and good for Barrie. He is improving all the time, which is great.
"He has progressed well recently and hopefully there is plenty more to come from him between now and the end of the season."
Meanwhile, Morton are expected to today confirm prices for the re-arranged Doonhamers clash after the game was rescheduled for tomorrow night following the death of 74-year-old Ton supporter Andrew Kemp at Cappielow on Saturday.
A statement on the club's official website said: "Further details regarding the match and admission arrangements will be posted here tomorrow [Tuesday] once confirmed."