Funding for the new hospital is being made available under the national eradicating dormitories programme.
It has also submitted an outline planning application for a second phase on the same site which could potentially provide a further 72 beds, depending on further funding becoming available in the future.
The NHS East Sussex Clinical Commissioning Group (CCG) and Sussex Partnership NHS Foundation Trust (SPFT) held a formal public consultation into the proposals between June and September 2021 - and hundreds of people made their views known.
The NHS said most people who responded to the consultation strongly supported the proposals, with the site in Mount View Street being the preferred location.
A further pre-planning consultation with residents living near the site was held in March 2022. The NHS said most people either strongly agreed or tended to agree with the plans to build a new mental health hospital on the site.
Most people also either strongly agreed or tended to agree with plans to potentially extend the site in the future to create a campus to provide all hospital-based mental health services in East Sussex, according to the NHS.
There were some objections to a new mental health hospital on the site. Residents expressed concerns about, among other things, access roads, traffic levels and impact on wildlife.
The NHS said these concerns have been addressed in the formal planning application.
Programme director Paula Kirkland said: "This planning application marks a major step forward towards implementing the first phase of our wider vision to create new modern facilities to address all inpatient mental health needs on a single site for people across East Sussex and beyond.
"We are delighted that most people we have consulted have agreed that there is a need for a new mental health hospital and that the land in Mount View Street is a suitable site for the new facilities. Obviously, local people have some specific concerns but we are confident we can address those as we progress with our plans."
People have until June 19 to comment on the plans.