Once again, what brand computer is it? I really would like to know that.
Unless I am missing something, I don't think you can combine the two 1TB drives. They are different drives not a partition. You could connect them with RAID, but even with a RAID1 (which would be great) you would lose 1TB of space. But, they don't need to be connected. The first drive would house the OS and anything else. The second drive would be accessible in a seamless fashion.
Once you are set up with the drives, clone the old drive with cloning software and restore it to the first drive. You will have to expand it after, but that is fairly easy.
The other thing you could do is scrap the first 1TB HDD and get a Samsung 1TB SSD. Mine didn't cost all that much, and it was two years ago. You could install the OS and databases and read/writes would be much faster than on the spindle drives. The other advantage would be the cloning process. The cloning software for SSDs is amazingly simple. They come with a kit. You connect a USB drive to the new SSD. Run the software. Choose drive A (in the computer) and select clone to drive B. Runs in 45 minutes. Disconnect drive B and put in new server. Done. There may be drivers and a few tweaks.
If none of this is doable, $220 is ridiculously cheap to have it done and done right.