You can say it is the law of nature.
I do not know if you can accept the following explanation:

Light is electro-magnetic wave. It is the change of electric field which cause the magnetic field produced at near by space (the direction of induced magnetic field is perpendicular to electric field).
And the change of magnetic cause the electric field produced at near by space(the direction of induced electric field is perpendicular to the magnetic field).
Think about the direction of electric/magnetic flux and you will know the distribution of induced magnetic/electric field. 
And the above continuous process is what we called wave.
From the definition: we know it is a transverse wave. (I use other laws: Faradays's law etc. to explain the direction between E and B field)
Try to draw it by yourself on a piece of paper or look at it more closely at the simulation itself.