I have set up my accounts - Checking, Credit cards and Savings.
The accounts I want to be savings accounts have a Type of SAVINGS. However, I have noticed there are some accounts that have been set up as a Type of ASSET.

I have tried to change these accounts in the Edit Account - General tab window, but the account Type option is GREYED out so I don't appear to be able to change from account type of ASSET to SAVINGS.

Can anyone assist?

Thank you.

Does your account contain transactions? Asset accounts are for non-monetary items and I don't see how financial transactions would fit in there. If empty, create a new account and just get rid of the asset account. If not, you can select all existing lines and move them to a new savings account (right-click, move to...) but I don't know how it'll interpret the lines of the ledger.

I was about to suggest the same as zebulon. Create a new account with the new type (you can adjust the name later if needed), open the ledger of your existing account, select all transactions and move them to the new account. If the account is not referenced in other places (reports, ...) you should be able delete the old account. Now would be the time for the name adjustment. Does that make sense?