The move will require significant redevelopment of the famous old ground, which is still the home of Swansea RFC, to initially increase the current 4,500 capacity to around 8,000.
Bradley would not be drawn on exactly how the project would be funded.
“We are not talking about the details of the financing,” said Bradley.
“It is in place and the council have invested in the stadium which we are pleased and grateful for and we will take it on a long-term lease.”
The Welsh rugby club previously announced they would be moving from Swansea.com Stadium to the smaller St Helen’s venue for the 2025-26 season.
Ospreys will not start the campaign in their new home because Swansea Cricket Club will continue to play at St Helen’s until the end of their 2025 campaign before moving to a new ground in the city.
That means Ospreys’ first home game at the new venue will take place a few months after the 2025-26 season has started.
They will have to play any home matches between September and November at alternative venues.
“We can’t start doing the pitch until Swansea Cricket Club have finished their season so that is the end of August,” said Bradley.
“So then we will install the stands and put the pitch in.
“That will take up most of block one of URC (United Rugby Championship) games before the autumn internationals.
“We expect to be able to move in during November so our first games there are going to be at the beginning of block two.”
