For future reference you can go to the motherboard page, CPU Support, then find the list of supported CPU's which includes the BIOS version needed:
https://www.gigabyte.com/Motherboard/GA-Z87-HD3-rev-1x#support-cpu
*Also, what does an i7-4790K cost?
Last I checked they were hard to find and cost between $400 and $500 new, and at least $200USD used.
You can get an R5-2600, motherboard and 16GB DDR4 (i.e. 2x8GB 3200MHz DDR4) for roughly $350USD.
https://pcpartpicker.com/list/Pzdpmq
Windows 10 license is now tied to your digital account (i.e. MSN) and there's a good chance now that simply moving your Windows drive to the new motherboard will work perfectly.
Not trying to push AMD but that does seem like a better option for the price. Sure performance in some games will be better on the i7-4790K but you get 50% more cores/threads with the R5-2600 which can help game smoothness and FPS in other games (especially as games need more CPU in the future) plus AM4 isn't dead yet and the Zen2/3000 series should be compatible.
*In fact, I'd consider doing what I said above but get an R5-3600 CPU instead later this year (which may be roughly 20% faster than the R5-2600).