Scotland's most senior judge Lord Gill, the Lord President, said it "makes sense in this day and age" to dispense with the garments in certain cases.
From April 22, judges sitting in the Inner House of the Court of Session in Edinburgh will no longer wear robes and wigs when hearing civil appeals, though they will wear them when hearing criminal appeals.
Lord Gill said: "In deciding to sit in civil appeals without robes or wigs the judges of the Inner House are in line with the practice of the United Kingdom Supreme Court.
"It makes sense in this day and age."
Advocates may also appear without wig and gown, while solicitors with rights of audience, who do not wear wigs, may appear without gowns.
The 11 judges sitting in the Inner House endorsed the change following a proposal by Lord Gill.
The Court of Session is Scotland's highest civil court and is divided into the Inner House and the Outer House.
The Outer House hears cases which have not previously been to court, while the Inner House is primarily the appeal court.
It hears appeals from both the Outer House and appeals in civil cases from the Sheriff Courts, the Court of the Lord Lyon, Scottish Land Court, the Lands Tribunal for Scotland, and other tribunals.