Owner George Pearson, 27, also wants to build ten houses close to the castle, with the land sale to financially support the development.
The plans signal a major step change for Dunnottar, a clifftop fortress where the Honours of Scotland were hidden from Oliver Cromwell's men during the 17th century. The castle was later forfeited by the Crown following the 1715 Jacobite rising.
The castle attracts 130,000 visitors a year, although facilities have remained limited. The plans will bring toilets, which sit within the castle site that is accessed down almost 200 steps, closer to the car park area.
The visitor centre, which will create 18 jobs, will have panoramic views over the castle, which sits on top of a 160ft cliff overlooking the North Sea.
The ten houses are earmarked for land opposite the main castle car park, to the southwest of Mains of Dunnottar Farm.
Mr Pearson said: “Careful thought and consideration has gone into not only the concept, but also the proposed design of the visitor centre, given its unique and historic setting.
“The economic benefits will be very significant. As I have said from the outset, to meet growing expectations, accommodate increased visitor numbers and importantly create an enhanced visitor experience, there has been a real need to build a dedicated facility.
“Crucially the proposals will provide a high-quality facility and new opportunities to showcase the fascinating role the castle has played in Scottish history.”
Mr Pearson is the son of Charles Pearson, a publishing tycoon and partner in major Aberdeenshire landholder Dunecht Estates, whose family first bought the castle in 1919.
The castle contributes £2.5m to the Aberdeenshire economy, with that figure predicted to rise another £1.4m if the upgrade goes ahead, documents supporting the application said.
Mr Pearson said he hoped work could begin on the development next year.