Why does the dipole moment of molecules go from positive to negative? In physics the dipole moment is said to go from the negative to the positive pole, check for instance https://en.wikipedia.org/wiki/Electric_dipole_moment (Elementary definition). 

This makes sense to me since in an electric field (which is directed from positive to negative) the dipole moment aligns with the electric field, such that in the aforementioned definition the positive pole points towards the negative pole of the electric field and vice versa. 
(also see: https://physics.stackexchange.com/questions/89157/motion-of-a-dipole-in-an-electric-field)

Now, in all representations of molecular dipole moments I could find online the dipole moment is directed from the positive to the negative pole. 

Check for instance: https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/Atomic_and_Molecular_Properties/Dipole_Moments

or just have a look at google images for the search term 'dipole moment molecule'.

This doesn't make any sense to me, is there any good reason for this discrepancy?
You have assessed the problem correctly. Physicists and chemists use just the opposite directions. Keep in mind that both are arbitrary choices, however the physicist's convention is consistent with electrostatics. All you have to do is to be aware of this direction in the chemistry literature. I have rarely seen any student ever thinking about it which is rather sad.

If you want more details read this article Misconceptions in Sign Conventions: Flipping the Electric Dipole Moment


  "Most chemists draw the direction of an electric dipole backwards. This inconsistency in sign convention is more than a trivial oversight or matter of convenience. We are introducing an incorrect convention that is central to our student’s understanding of fundamental thermodynamics; which way is up? As a student matures from general chemistry to organic through analytical, physical, inorganic, and biochemistry they are reintroduced to similar, powerful concepts that hold our discipline together. However, this reconnection of chemical principles comes with each subdiscipline’s own idiosyncrasies and a highly contextual framework. Reexamination of a central concept from the perspective of a new subdiscipline should not introduce misconceptions about that concept. When misconceptions introduced through chemical language can be avoided, we should change the way we speak."