The two can be chosen, according to taste, from a list of three: the speed of light, the strength of gravity, and Planck’s constant, which relates the energy to the frequency of a particle of light, say George Matsas of the São Paulo State University and his colleagues.
Once two constants have been chosen from that list, they say, those are the only parameters that need have units of measurement ascribed to them. Everything else — for example, the charge or the mass of an electron, or the strength of nuclear forces — can be described in relation to these two 'dimensional' constants.
So far, as far as I know, this work hasn't been published yet, only appearing on the e-print arXiv. So we will have to wait until it does to see the kind of reaction and feedback it will get.
It would be interesting to compare this to an earlier manuscript titled "Trialogue on the number of fundamental constants" by M. J. Duff, L. B. Okun, G. Veneziano, where they also argue with each other on the actual number of fundamental constants that is really needed to describe our universe. It certainly would make a very interesting reading if one is getting sick of the upcoming holiday festivities!