Depends.
If they were installed using Steam, just reinstall the Steam client and update Steam settings to point to the folder you have all the games in so that it recognizes them and adds them to the library.
For other games that are like MMO's and have their own client, just make sure you point the install folder to where you installed it and it will just run a check on all the files.
Same method for other clients like Ubisoft, EA Origin, etc.
For some other games purchased from places like GOG where it installs stand alone just navigate to the folder where it is installed and then make a new shortcut to the executable on your desktop.
Then there is those weird outliers that have their own installation client that need to re download everything again.
But those are very few out there and chances are you don't have any of them or only a couple.
However, you shouldn't need to do a clean install of Windows if it's already in working condition.
Just plug it into the new board and boot it up.