The projects are located in north-west Scotland. Beatrice is being developed by SSE and Sea Energy, and Moray Firth by EDPR and Repsol.
The decision is a boost to the 1GW Beatrice project after it, along with the 340MW Galloper, was left out of the UK government's "provisionally affordable" list of projects.
It has been reported the projects are worth up to £2.5 billion (EUR 3 billion) to the Scottish economy.
A series of applications has been submitted to the Scottish authorities, aimed at re-opening the port of Ardesier as an offshore wind manufacturing, installation and operations and maintenance (O&M) base.
Ardesier's advantages include 138 hectares of vacant land, a 1-kilometre walled deep-water quay and its close proximity to the Moray Firth offshore wind zone.