Animation software and eLearning

If you want to go fully bespoke you could try Adobe Animate (formerly Flash). It now has HTML5 output and can be embedded in to Storyline as a web object.

http://www.adobe.com/uk/products/animate.html 

Nick is right to bring After Effects to the table. It has a lot going for it and if used properly will give you a very polished finish. One consideration before diving in though, be sure your hardware is up to the task. Render times can be very long on an underpowered computer and will potentially prevent you using your machine until the render has finished.

Another plus in my mind for Adobe Animate is the HTML5 output. One minute of HTML5 animation will consume significantly less bandwidth than a one minute video. In a test I carried out a few months ago 1 minute HTML5 = 3.4MB vs 1 minute of video = 14.5MB. HTML5 animation quality is also lossless when scaled up too.

For the benefit of comparison here is an animation we built in Adobe Animate: http://www.4-pt.co.uk/samples/html5-animation/character/index.html 

As with everything, one size doesn't fit all. HTML5 animation might work well for one brief, video might work better for another (e.g.maybe your video will live on YouTube or contains footage).

Regardless of which of the two is used you'll need to generate your graphics first. We use Adobe Illustrator for this although I'm sure there are plenty of other programmes that can do a similar job.

The other thing you need is an animator.  The tool with the style you've shown is really just ink and paint, it's more about who is creating the work frame by frame, even with helpful tools like AE. If you're in the UK the Royal College has amazing grads. 

Additional to all the great tools mentioned here, I have to say GoAnimate is my jam! It has a ton of capabilities unless you really want to draw your own characters.

I agree with you. I use all the tools people have mentioned. I can get some good results but it is time-consuming and not nearly as good as a skilled animator could.

We use Crazytalk Animator from Reallusion.  No monthly fees and lots of add on packs, characters, scenes, props available.  We went the whole hog and bought a motion camera for an Xbox, linked it through iClone and can port custom motions through to Crazytalk Animator.    Not really necessary, but we did it for R&D purposes for a proof of concept.

We can export mp4 videos from Crazytalk and add them directly to Storyline or host them on Vimeo and add as a web object.

I've used Powtoon for the last 18 months, very user friendly and versatile! If you have access to Adobe Creative Cloud its very straightforward to get the Powtoon assets into Storyline.

However, if you want to really get into animation. I'd recommend this

https://videohive.net/item/design-and-motion-character-kit/20838034

All the power of After Affects - with a nice UI!