I thought that's what everyone always figured? seems kinda obvious.
Well, no.
That everyone emigrated from Africa & thus immigrated the rest of the world is accepted, but some believe(d) that those humans that settled into Europe 45000 years ago developed agriculture independently or copied from Middle-Eastern & Asian cultures.
Scientists have apparently been arguing whether we've descended from European hunter-gatherers or European farmers, but this article proves that there never was such a thing as a European farmer.
By comparing DNA they've been able to prove that the DNA that was very common amongst the hunter gatherers is very rare amongst the (Central) Europeans of today and that the DNA belonging to the early farmers is more common (although it would be wrong to claim that they're our ancestors, since there's still not a 100% match).
What I don't see in this article is if/how they took immigrants that arrived after agriculture had already become well known across Europe & often replaced (killed) previous inhabitants into account. Take the Huns, Slavic peoples (first mentioned in the 6th century AD by Ptolemy, so it's reasonable to assume they immigrated), etc. & whether they took DNA samples from Iirsh & Scottish people (Mostly descendants from Celtic & Pictish peoples, the dominant peoples of Europe, even after agriculture had become well known.)