Technically I think he's still just the 'presumptive' one, since the convention won't happen for a while. He has the delegates, though, to have secured it.
Hillary hasn't stepped down yet though.
I didn't see it, but you can read a transcript here
Obama's speech on the occasion of becoming the presumptive Democratic nominee for the President of the United States
It's very inspiring.
I really hope he doesn't take Clinton on as VP. All of the stuff that's happened during the primaries has destroyed her credibility as a candidate and I doubt she could be trusted in office.