Despite how simple it seems, needs vary from implementation to implementation.
Maybe yours has spine animation instead of frame animation, or a combination. Maybe it has 3D lighting. Maybe it needs additional information per-frame for some reason, like knowing where a weapon/tool/clothing is attached.
That said, there are commercial products like Spine that have formats that are at least visible to the public, if not open for general use. http://esotericsoftware.com/spine-in-depth
You might be looking for something like Spine. Sprites are broken up into smaller parts and those smaller parts are moved around like a skeleton.
Omnicrola is correct. It is dependent on engine, for example if you are using Unity, Mecanim system has that in mind, so you can setup the transition between the two moves with a curve that "mixes" both animations kind of thing (as far as I know).
If however you aren't working with Unity and you are working with normal sprite movements, you'd need to create the frames to transition between the two animations. That is one way.
The other is to use an external animation program to help you out in the blend. I don't know the exact way or if there is a specific software that does that as I just started doing animations like 4 hours ago XD but from what I can understand you have Spine but this one is geared for skeletal animation more than anything. You also have Toon Boom which I am thinking of trying.
Finally, I just found out this: http://www.gamasutra.com/view/news/176663/5_tips_for_making_great_animations_for_2D_games.php
Not sure if that is of any help, hope so though. :)
Yes, the game is made in Unity with Spine for the character animations. All of the Pixel Art is by Jay Knox and the soundtrack is composed by Mike Clark. Very happy with how it's turning out.
Alternatively he could grab something like Spine and use their runtime integration for either base Unity or 2DToolkit. But that's a little more fancy and expensive...