Are you using UEFI bios or legacy BIOS? For using GPT your motherboard must have UEFI BIOS. This will also require that your OS is installed by booting the install media in "UEFI mode". That means after you convert your partition table to GPT, you must reinstall your OS. The reason you need to reinstall it because on UEFI BIOS, OSs use a special EFI boot partition where the bootloaders are stored.
As for the actual conversion, you can use the gdisk utility in linux (run it from a live USB to be safe). It will detect an MBR partition and convert it to GPT without any additional changes. Though this is fairly straightforward, it's still better if you backup all your data just in case.
Of couse, the safest way to do this is to wipe your HDD and reinstall the OS after enabling UEFI BIOS on your motherboard.