That may work. But with a few conditions.
Here's the thing. The Optiplex 990 came with the i7-2600 as an option. Since the only real difference (aisde from TXT or VT-d support, which most people don't need) between the i7-2600 and the i7-2600k is the ability to overclock and the better integrated graphics there isn't any reason your motherboard shouldn't work with the i7-2600k. It's the rest of the components in your system that are more uncertain.
First, your PSU. This is a minor concern but worth bringing up. While the i3 you're using and the i7 you want to use have a very similar power draw at idle (roughly 77 watts), when under full load the i7 can pull down roughly 40 watts more power than the i3. I would imagine your stock 250w PSU could handle the difference, as it's the only option for the DT build and that did come with an i7 option, but it's something to keep in mind.
Second, and this the bigger of the maybes. Your i3 has a much lower TDP (65w) than the i7 TDP (95w). So the stock cooler may not be enough for the increased thermal load of the i7. If Dell had different CPU coolers for the different CPUs, you may not have the ability to properly cool the CPU. But if they just made one cooler to handle all the different options, then your chip would be within the range it could cool. It would make sense to me to just use one cooler for the entire series, but sometimes Dell does weird things.
So while your computer is compatible with the i7-2600 and likely compatible with the i7-2600k, other parts might have a harder time keeping up. So you can roll the dice and see if it'll work if you like. I would recommend making sure your system has the most up to date BIOS to assure compatibility.