Have you tried just stepping away from the monitor and looking out the window? It sounds obvious, but it really works, because the problem isn't so much the screen itself, but the fact that your eyes are constantly strained at the same distance. When you look far away, the muscles relax. The double vision appears precisely because those muscles can no longer contract in sync - they're just exhausted.
It won't go away on its own, I agree with the previous answer. But even if you don't do anything, your vision won't drop drastically - it'll most likely just stay at this level of discomfort and fatigue. Here's what really helps: every hour, get up and look at something distant for about five minutes. Don't just get distracted, actually focus on far objects. Plus blink more often - people blink way less at the monitor than normally, and the tear film dries out.
There's also a life hack - if possible, dim the lights in your office and don't keep your monitor brightness at maximum. The contrast between a bright screen and the dark surroundings is a separate source of eye strain. And if the double vision doesn't go away even after breaks, you should see an ophthalmologist - you might need glasses for computer work.