The consortium developing the project, Smart Wind, submitted its application at the start of February.
Smart Wind is a 50:50 joint venture consisting of Siemens' financial serives unit and Mainstream Renewable Power.
The second phase of the 4GW, Round Three Hornsea Zone is planned with 360 turbines.
In December, UK energy minister Ed Davey gave consent for the construction of the 1.2GW Hornsea 1. It is expected online in 2019.
Earlier this month, Dong Energy bought out the consortium partners in the Hornsea 1 project for an undisclosed fee. Dong had acquired a 33% stake in the project in 2011.