Do you just want to transfer documents on there or programs as well? Usually for situations like this , you can buy an external HDD enclosure and put the old drive in there and read it as an external drive. Also BB offers GS Data Backup Services, but I dont know their pricing structure as I have not had to utilize these services at all.
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Why replace? unless it's a laptop, why not just add the new hardrive? Oh well, maybe you have reasons. Yes, you can migrate all the data from your old h.drive to the new h.drive including your OS. The new hardrive should come with a utility, for you to be able to that; or you can use third party software like Norton Ghost and the like.