The two projects are Centrica's 580MW Race Bank and Warwick Energy's 560MW Dudgeon wind farm in the Greater Wash. The third, Centrica's 540MW Docking Shoal, has been rejected for environmental reasons.
In a statement, the Department of Energy and Climate Change said Docking Shoal had been refused as a result of the potential impact to Sandwich Terns, a seabird that is protected by environmental legislation.
Speaking about the decision, "These two projects will not only bring us considerable amounts of clean energy, but significant investment and jobs too.
"We have also shown that we are mindful of other consequences, such as the impact on bird populations, in deciding that it would not be appropriate to consent all three applications."
The three projects were part of five planned for the area, representing around 3GW of potential capacity and representing around £7 million investment. The other two wind farms are Sheringham Shoal and Triton Knoll.
In February, RWE Npower submitted an application for the 1.2GW Triton Knoll wind farm to the UK's Infrastructure Planning Commission (IPC).
The application will now pass into the IPC’s examination process. RWE Npower’s submission included details of the feedback from its 42-day consultation exercise.
In 2010, industry and government agreed to fund a new £20 million radar system for the Ministry of Defence (MoD). The MoD had vetoed the offshore projects in the Greater Wash off the east coast of England, objecting to the clutter effect that the turbines' rotating blades would produce on its air defence radar screens.