That is how stereo is supposed to work. Your left ear is hearing the left signal before the right signal, and vice versa. The shape of the head and psycho-acoustics also have something to do with it.
The key is to start with speakers that image well. In my experience, narrow baffles and low diffraction help with imaging. Concentric drivers also help with imaging.
I have KEF LS60 Wireless speakers in my office, which have both narrow baffles and concentric midrange/tweeter drivers. They image extremely well. If you have a dealer anywhere near where you live, do yourself a favor and go listen to them.
In my family room I have heavily modified ELAC UBR62 Uni-Fi Reference speakers. They also have concentric midrange/tweeter drivers. They are not as narrow as the LS60s, but they have convex baffles, which help to reduce diffraction. They imaged well out of the box, but improved with the modifications I made.
Lastly, DSP can help to improve imaging, for example by correcting for imbalances between the left and right channel frequency responses due to asymmetrical room reflections or slight differences in the left and right speaker drivers.
With my Elacs in my family room, DSP did improve imaging. Specifically, there are asymmetries due to the layout of the room and the speakers are not the same distances from the side walls. Without DSP there are significant differences between their frequency responses as measured at the listening position. I used DSP to tune both the left and right channels to the same target curve, and now they closely match.
I sit close to my LS60s in my office, and the imaging is great even without DSP. For those, I used DSP mostly to correct for room modes and to adjust the high frequencies a tad to compensate for not being able to toe them in much due to furniture being in the way.
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