Manipulating biological samples in microliter droplets has vast potential in molecular diagnostics. We present a system for the two-dimensional (2D) magnetic manipulation of aqueous droplets suspended in silicone oil as a platform for on-chip bioanalysis. Superparamagnetic microparticles inside the droplets provide the means of the magnetic actuation. The droplets can be displaced, merged, mixed and separated on the chip without the use of external moving magnets or parts. In our system three-dimensional surface structures are replaced by an optimised hydrophilic/hydrophobic patterning of the chip surface to facilitating droplet splitting. We compare the functionality of the droplet manipulation system for magnetic particles of different sizes and demonstrate a dependency between particle size and performance. Finally we present the potential of the proposed system in droplet-based biomedical analysis by performing the dilution and detection of the secondary antibody of an enzyme-linked immuno-sorbent assay (ELISA) on-chip.