The answer is almost certainly yes. In 99% of cases, you can use that cookware on your normal stove. In the remaining 1%, you can't, but being induction-ready is not the reason why you can't, it just so happens that there are some designs which won't work on a normal stove but will work on induction.
Being induction-ready means that it is made of a ferromagnetic material (or, for sandwich-bottoms, contains a sheet of ferromagnetic material). If you can stick a magnet to it, then it will work on induction. So, in reality, many pots and pans were induction-ready long before there were induction stoves. They were made of stainless or enameled steel, or of cast or forged iron, and that made them suitable for induction. While not every traditional material works with induction, every induction material works with traditional.
The last small percentage that won't work with a traditional stove is not due to material, but due to shape. Take for example a cast iron pan in a shape that is very widespread in the US, with a short iron handle, tiny spout-like indentation on both sides, and a 2 mm high lip circling the bottom. This lip is what makes the pan terrible on an electric stove. It creates an enclosed space between the hob and the pan, into which the hob blasts heat. Not only do you have trouble with properly heating the food (because you now have a thin layer of great insulator - air - between the pan bottom and the heat source), it can also heat up so much that it can melt a ceramic hob. In some other specialized cookware, there is no such enclosed space, but the surface curves away, for example in some induction woks. Since induction heats contactless, that's not a problem, but the electric stove won't manage to heat properly the parts which are not in direct contact.
So, to summarize: If you have a standard pot or pan with a flat bottom that comes in contact with the stove, everything is fine. It will always work on the standard stove, including those which have an induction-ready label. If you have a bottom shape that leaves gaps between large portions of the bottom and the stove, you will have to find out more about the consequences of using it on an electric stove.