Hi,
Unlike Dropbox, Onedrive cannot detect other systems on your local LAN and then sync more quickly vs. pulling down from OneDrive servers. So, to make things go faster, you could copy the files over manually before turning on OneDrive then select that folder where you copied your data. When you enable Onedrive, it will then see the files are already there and only sync the delta's.
From there, you can blow away your old system and you're good-to-go.