I just recently purchased a Dell XPS 8300, and I plan on upgrading it very soon...in fact I just installed a corsair cx600 power supply the other night.
Now I'm waiting for my new card in the mail; I chose a Radeon HD 7850.
I've asked this question before on which card would be suitable for my pc, so now I'm just double checking to be safe.
Yes, it will work fine, as long as the mobo has a PCI-Express x16 slot (Long slot), then you are good to go. Make sure to connect the PCI-E power connectors into the card and everything should work fine after you install the card and install the correct drivers.
Another thing you may want to watch out for is temperature. A 7850 is quite efficient, but still will run hot. Just be sure that your machine has adequate airflow and does not get clogged up with dust.