Can I transfer my purchased games to the PS4 by signing in with same PSN account?

Games belong to PSN account and not to specific PS4 device.

Once you login to your new PS4 with your old PSN account, go to Library and you will be able to download your games (see Download PlayStation Store Purchases to the PS4).

If you want to avoid downloads, you can bring your games via external HDD or flash drive (see Can I copy PS4 games to USB stick (not external hdd)?)