Restore document files from a Time Machine Backup

When you buy your new Mac and turn it on, it will ask if you want to transfer information from another Mac or its Time Machine backup. Select that option. It will present you with the opportunity to transfer selected items, such as your User Account and all its data, exactly as you propose. Click the "reveal triangles" in your User Account to expand the selections.

Refer to Step 4 in Set up your new Mac - Apple Support.

One approach you can take is to setup your new iMac with the same user name and password as your old machine and name the hard drive the same. Open the Documents folder on the new machine, enter Time Machine and access the backups from the old machine. Make sure you're in the Documents folder, do a Select All, ⌘+A, and restore to the Documents folder on your new machine.