The Reimagined Battlestar started as a remake, or reboot (no real difference) to the original Battlestar Galactica. Due to changes in audience expectations, it was grittier, more realistic than the original. No preachy moral of the week or happy go lucky attitude, light on the reset button, no kid and his dog bot. It has obvious changes, as the Cylons were now human creations who rebelled, instead of creations of a Lizard species of the same name.
But Battlestar has a reoccurring theme of "All of this has happen before, and all of this will happen again". The myth in the series says that there was an original planet, and a war. They escaped to form colonies. The main 12 colonies are destroyed, and a 13th colony that once was lost is found. And then the cycle starts again.
So they form doubt on whether it's a reboot or a sequel. They imply that the original happened some cycles ago, and the reimagined series is another cycle of the same. Keep in in Galactica 1980 had the Battlestar Galactica crew finally find the 13th colony, Earth, And one episode had an android, a human formed cylon. In the reimagined series, they have one part where old school Cylons are seen, the Cylons Centurions used in the old series.
Furthermore, they also state (a bit more than just imply), that one girl in the new series is mitochondrial eve to real life us. Edward James Olmos has also jokingly implied that Blade Runner is a sequel to the new BSG vis-a-vis his character and Replicants in that movie but that's beside the point.
Question is, is there an official, word of God statement that the reimagined series is a sequel, in-universe? That the events of the old series actually happened and are in continuity?