The card is 10.2 " (259.1mm) long but I couldn't find anything on the case so try this: Measure the distance between the back of you computer and the point the GPU would hit if it was too long. If thats more than the GPU's lenght, it'll fit.
EDIT: Also yes, you'll have to upgrade your PSU but those are standardized in size so you wont have to worry about that.