Tremendous progress has been made recently in imaging the contacts between intra-cellular organelles, which are thought to be mediated by soluble tethers. However, they are still difficult to study in cellulo , and reconstituting them in vitro is a standing challenge. Here we take a mimetic approach to study Giant unilamellar vesicles (GUVs) and supported lipid bilayers (SLBs) interacting via single- (or double-) stranded DNA sequences of two different lengths. Like intra-cellular tethers which may reside in the cytosol when unbound, the DNA-tethers are soluble, but can insert into the membrane with the help of cholesterol moieties found at their extremities. Tether-exchange between the bulk “cytosol” and the GUV/SLB membrane leads to a novel statistical ensemble in which the entire system equilibrates together, rather than individual GUVs behaving as separate closed systems. As a consequence, adhesion between the GUV and the SLB is driven by collective entropic effects amplified by tether shape changes associated with membrane bridging. A direct experimental consequence is an unusual dependence on tether-concentration, which becomes an important control parameter at low concentrations, while tether length/flexibility are less important. The establishment of this fundamentally different interaction between two membranes suggests that in physiological conditions, the regulation of contact formation inside cells may be very different from the case of the much studied ligand-receptor mediated cell adhesion.