Having moved to Office 2016, I had to first install Office 2010 to a virtual test machine to get screenshots. Here we go, this is the the process which you have to repeat for each notebook you want to open in Windows 10 built-in OneNote app.
1.) If your notebooks are already stored in OneDrive, jump to step 7. If they are stored locally, open OneNote 2010.
I created a simple Sample Notebook to show this process:
(Click screenshots to enlarge)
2.) Open the File menu, select Info > Share on Web or Network:
3.) Select Web, click Sign In:
4.) Enter your MS account credentials:
If you have enabled two-step authentication
on your MS account, you need first create an app password
and use it here instead of the MS account password.
5.) Select in which OneDrive folder you want to save the notebook, click Share Notebook:6.) Close OneNote 2010
7.) Open Windows 10 OneNote app. If you sign in to Windows with a Microsoft (MS) account, jump to step 11. If you sign in with a local account click Personal Microsoft Account:8.) Sign in to your MS account:
'9.) Enter your Windows password, click Sign in to just this app instead:
10.) Click Start using OneNote:11.) You can now start using Windows 10 OneNote app, having access to your notebooks:
This is important! Do not click Next here, it will convert your local Windows user account to an MS account!
Remember that you can also use, access and edit your notebooks stored in OneDrive online at outlook.com:Kari