The decision by ministers overturns a recommendation from a Scottish government reporter that the Pentland Studios Project should be thrown out.
Midlothian Council had failed to make an initial ruling on the application.
PSL Land Ltd said it was "very pleased" with the decision and hoped the first studio facilities would be operational by late 2018.
The studio is earmarked for a site at Old Pentland Farm, near Straiton.
The Association of Film and Television Practitioners Scotland (AFTPS) had called on ministers to back a new studio.
PSL land Ltd said: "PSL Land Ltd are very pleased with today's decision by ministers to approve the grant of planning permission in principle for Scotland's world-class Film & TV studio complex, and will be moving forward immediately with the application for planning permission in detail for the Film Studio, Academy and Energy Centre sections of the development.
"Working together with Midlothian Council, PSL hope this next stage will be expedited accordingly, recovering the construction scheduling that will enable delivery of the key Studio operation by late 2018.
"It is anticipated that a detailed schedule to progress the planning application will be agreed with Midlothian Council in the next few weeks, producing a phased timeframe with the Studio, Academy and Energy Centre as the first buildings to be progressed to full planning consent."
The Association of Film and Television Practitioners Scotland, which represents some of those working in film and television, previously said it believed the sector was being badly affected by the lack of a studio space.
Planning permission has been granted in principle for a film studio to be built on the outskirts of Edinburgh.