It means regular live terrestrial coverage is due to end next season.
The Guinness PRO14 has yet to confirm the new deal, but BBC Scotland stated: "BBC Northern Ireland, BBC Scotland, BBC Wales, BBC Alba and S4C put together a competitive joint bid.
"We are therefore disappointed our bid has been rejected."
Edinburgh and Glasgow Warriors games have been broadcast regularly on BBC Alba, with some also being screened on BBC Two Scotland.
BBC Alba's extensive and high-quality coverage will be missed by Scottish rugby fans and a tough and will be a tough act to follow.
BBC Two Northern Ireland had also broadcast games involving Ulster.
Live games involving the four Welsh sides will also end on BBC Two Wales, but negotiations over Welsh language rights are continuing with the possibility of some games being broadcast on S4C.
The BBC still hopes to be able to continue to offer highlights.