This is something I did, short-term, in this year. It should be doable, but there are caveats.
TheFirst, you amend the contract
My contract with the company specifies that I work in my home town. When the work-from-home became mandatory, everyone in my company signed a contract amendment that allowed for remote work. Since you are already working remotely, talk to your manager about fixing this in writing. I see no reason why they should object.
Moving awayThen, you talk to your manager about moving
It is well within your rights to move to another city, but I advise talking to your manager while you finalize your plans. Moving will take some of your time, you might be away from some of your belongings, your habits might change, your Internet connection might be worse than before, you might be tired more often. This, typically, will not cause (huge) problems with your productivity, but your manager should still be aware of that. Your best bet when talking to your manager is letting them know that you foresee these problems and you're taking steps to mitigate them.