This is the most obvious and preferable route. Download any documents you have in your MySite and move them to a location or folder within your OneDrive for Business instance on Nexus365.
To access your OneDrive for Business instance, log in to Nexus365 and click on the Waffle (the little grid of dots in the top left hand corner) and then select OneDrive from the menu.
Your OneDrive for Business instance will have a URL like the following: https://unioxfordnexus-my.sharepoint.com/personal/<youroxfordusername>_o...
Please ensure that if you are moving any documents from your MySite to OneDrive for Business that you familiarise yourself with the information governance guidelines around any sensitive or personal data: Information Security guidance and policy