To be absolutely sure, you need to check the following:
* Bolt Pattern: This refers to the number of lug nuts and the distance between them. Find this information for both the 1999 GMC 1500 and the 2004 Chevy 1500 wheels. They *should* be the same, but it's crucial to verify.
* Wheel Offset: This is the distance between the wheel's mounting surface and the centerline of the wheel. Significant differences in offset can affect handling and potentially cause rubbing against suspension components.
* Center Bore: This is the diameter of the hole in the center of the wheel that fits over the hub. A too-small center bore won't fit, while a too-large one might need hub-centric rings.
You can usually find this information on a sticker on the driver's side doorjamb (for the 2004 Chevy) or etched into the wheels themselves. Alternatively, a quick online search using the year, make, and model of each truck should provide this information. If you have the specific wheel specifications from the 1999 GMC 1500, comparing them to the specifications of the 2004 Chevy 1500 is even better.
In short: Don't assume they'll fit. Always verify the bolt pattern, offset, and center bore before attempting to mount the wheels.