Functional reconstitution of membrane proteins within lipid bilayers is crucial for understanding their biological function in living cells. While this strategy has been extensively used with liposomes, reconstitution of membrane proteins in lipidic cubic mesophases presents significant challenges related to the structural complexity of the lipid bilayer, organized on saddle-like minimal surfaces. Although reconstitution of membrane proteins in lipidic cubic mesophases plays a prominent role in membrane protein crystallization, nanotechnology, controlled drug delivery, and pathology of diseased cells, little is known about the molecular mechanism of protein reconstitution and about how transport properties of the doped mesophase mirror the original molecular gating features of the reconstituted membrane proteins. In this work we design a general strategy to demonstrate correct functional reconstitution of active and selective membrane protein transporters in lipidic mesophases, exemplified by the bacterial ClC exchanger from Escherichia coli (EcClC) as a model ion transporter. We show that its correct reconstitution in the lipidic matrix can be used to generate macroscopic proton and chloride pumps capable of selectively transporting charges over the length scale of centimeters. By further exploiting the coupled chloride/proton exchange of this membrane protein and by combining parallel or antiparallel chloride and proton gradients, we show that the doped mesophase can operate as a charge separation device relying only on the reconstituted EcClC protein and an external bias potential. These results may thus also pave the way to possible applications in supercapacitors, ion batteries, and molecular pumps.