Switch from old to new iMac

Migrating from your Time Machine backup is the easiest, fastest and most reliable way to migrate to a new iMac.

see > How to move your content to a new Mac - Apple Support

Then to make your old iMac ready for another user.

see > What to do before you sell, give away, or trade in your Mac - Apple Support

What he said +1. Did this myself a few months ago from a 9 year old 21.5" i-Mac to a new (Apple refurb) 27" i-Mac, and it worked flawlessly with migration Assistant. Just be aware, some of your old software may not run on the latest Mac OS. If they are mission critical to you you may want to see if they are compatible to what you intend to upgrade to or if there is a free or paid update of them available.