The direct answer would be to enable reviews based in product purchase and nothing else. We did this for a site (they don't review products, but the seller/buyer, however the same principle applies) and here's the gist of it: Since we want to encourage people to review, when people enters their profile's dashboard, the first thing they see is a small dialog box with operations to review. We have 3 options (buyer, seller, counterpart review), but in your case only one is enough. I've included the 2 possible options in a single element as a quick mock up, but you'll obviously need one or the other.
And obviously, when you click to review, you'll have a list of products to review.
Again, keep in mind you might not require this, while for us, it's of upmost importance. The point is: you only allow reviews if the product has been purchased, and that's what this system is aimed to.
As an additional option, Envato does this: they allow everybody to review something since they have online digital previews. However, it's clearly stated if the reviewer has purchased the product or not. I don't like this approach since it's prone to abuse and requires heavy moderation, but in case you can't change your backend code, it's a reasonable option.