Two-dimensional fluorescence spectroscopy (2D FS) is applied to determine the conformation and femtosecond electronic population transfer in a dimer of magnesium meso tetraphenylporphyrin. The dimers are prepared by self-assembly of the monomer within the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine liposomes. A theoretical framework to describe 2D FS experiments is presented, and a direct comparison is made between the observables of this measurement and those of 2D electronic spectroscopy (2D ES). The sensitivity of the method to varying dimer conformation is explored. A global multivariable fitting analysis of linear and 2D FS data indicates that the dimer adopts a "bent T-shaped" conformation. Moreover, the manifold of singly excited excitons undergoes rapid electronic dephasing and downhill population transfer on the time scale of similar to 95 fs. The open conformation of the dimer suggests that its self-assembly is favored by an increase in entropy of the local membrane environment.