Can I apply a CSS transition on hover-out only?

Here's one way to achieve this (put a bogus property none for transition property in :hover):

#inner2{
    opacity:0;
    transition:opacity 2000ms;
}
#outer:hover #inner2{
    opacity:1;
    transition:none;
}

http://jsfiddle.net/j716sbav/4/

Answer updated to incorporate @BoltClock's suggestion. Putting none instead of a bogus property is definitely more elegant.

I know this is a very old post but, as it came up in response to my Google search on the subject, I thought I'd post my solution.

After reading everything posted here, I found the simplest solution. Place a transition on the initial state as follows:

.btn {
  opacity:0;
  transition:0.6s;
}

.btn:hover {
  opacity:1;
  transition:0.8s;
}

So it has a transition time to the hover state and a transition time to the non-hover (ie normal) state. Saves a whole bunch of code.

If you prefer not to specify the transition property more than once, you can apply the transition to :not(:hover), but the caveat is that you need to swap all of the other declarations as well:

#inner2{
    opacity:1;
}
#outer:not(:hover) #inner2{
    opacity:0;
    transition:opacity 2000ms;
}

Either of these will work, but if you don't want to deal with confusing inversions, stick with overriding via transition: none.

Also note that CSS selectors represent states and not events, which means that it utilizes a :hover state rather than mouseover and mouseout events; however, a transition from :hover to :not(:hover) is essentially the CSS way of expressing a mouseout animation.