Hello ! I'm Aymeric, an independent advisor, and I'm here to help !
It's absolutely possible. All you have to do is remove the hard disk from your old computer, then put it back in the new one.
Just make sure your PC can accommodate the hard drive: you'll usually need a SATA port and cable to plug the drive in.
Once connected to the new PC, you'll see the files present on the PC, and be able to browse them as if you were on your old PC.
Please let me know if you have any other question !