The widely expected move followed last month's defeat for HM Revenue and Customs (HMRC) in the long-running case.
A judge largely upheld a first-tier tribunal's ruling that substantially reduced a historic tax liability relating to 'oldco' Rangers. But the case will now go to another court.
An HMRC statement said: "We are pleased that the Upper Tribunal has given HMRC leave to appeal to the Court of Session.
"We continue to believe that schemes using Employee Benefit Trusts to avoid income tax and NICs (national insurance contributions) do not work."
The initial ruling decreed that a £46.2 million tax demand on Sir David Murray's Murray International Holdings company, most of which related to its tenure of Rangers, be substantially reduced as most of the payments could be construed as loans.
The disputed payments, made from 2001 to 2010, had left Rangers facing a tax bill that undermined Murray's final years as Rangers owner.
The club went into liquidation in June 2012, a year after Murray sold his majority share to Craig Whyte. Whyte's tenure ended with the club unable to pay separate tax debts totalling £21 million.
The ongoing legal battle does not affect the current Rangers regime.