What is the origin of the "positive-to-negative" convention concerning dipole moments in chemistry?
Some sources point out the direction of the dipole moment is convention dependent. Since both conventions are mathematically correct it seems important when solving a problem to identify the convention.  Both conventions seem to be derived from the bones of dead theories.

The physics convention does seem to have Franklin's work identifying negative "resinous electricity" and positive "vitreous electricity" as one step in the progression to the modern theory.  In modern theory a positive to negative electric field will orient a dipole such that the field is in the same direction as a negative to positive dipole.  

On the chemistry side, Peter Debye (who the unit for a dipole moment is named) developed the concept of the dipole moment in 1912 to explain anomalous dispersion. This dispersion was explained as being caused by a negative charge collecting on one side of a molecule leading to a dipole moment. This moment's magnitude explained anomalous dispersion, so direction did not seem to receive much attention.  Molecules during this time where described using the Thompson, or "plum pudding," model. In this model molecules were described as positively charged spheres.  (These spheres had no nucleus because the nucleus concept was in its infancy during this time period.) These spheres formed the basis of mathematical models used to describe the behavior of materials with a dipole moments.  The dipole moment in this sense went from the center of a molecule to the point of highest electron density.  With the center of the sphere as a pivot point, the rotation of molecules in an electric field could be explained. In this sense the positive to negative convention may be an artifact of the early spherical molecular models first used to describe dipole moments.  

sources:

J. W. Williams   Dipole theory and the size of molecules.  Trans. Faraday Soc., 1934,30, 723-728 

John W. Williams The Dielectric Constants of Binary Mixtures. VIII. The Electric Moment as a Vector Quantity, J. Am. Chem. Soc., 1928, 50 (9), pp 2350–2357  DOI: 10.1021/ja01396a005  Publication Date: September 1928

L. E. Sutton  Electric dipole moments and resonance in molecules, Trans. Faraday Soc., 1934,30, 789-801

https://www.quora.com/Why-does-a-dipole-have-a-direction-from-negative-to-positive-while-electric-field-lines-go-from-positive-to-negative

http://goldbook.iupac.org/E01929.html

http://www.ushistory.org/franklin/info/inventions.htm

http://www.wondersandmarvels.com/2011/12/accentuate-the-vitreous-eliminate-the-resinous.html