The scenario was that he would get extradited to Sweden, the case finds him not guilty, and then get extradited to the US. Assange tried to get the Swedish government to openly declare that this would not occur, and the Government replied that they could not make such statement. The argument generally comes that once existing legal proceeding are done, the agreement between Sweden and the US allow for extradition.

This exact same chain of events will now likely happen with the UK case. Once the case of the bail jump is finished and eventual punishment served, he will be shipped to the US.