We report on the search for anti-neutrinos of yet unknown origin with the Borexino detector at the Laboratori Nazionali del Gran Sasso. In particular, a hypothetical anti-neutrino flux from the Sun is investigated. Anti-neutrinos are detected through the neutron inverse $\beta$ decay reaction in a large liquid organic scintillator target. We set a new upper limit for a hypothetical solar $\bar{\nu}_e$ flux of 760 ${\rm cm}^{-2}{\rm s}^{-1}$, obtained assuming an undistorted solar $^8$B energy spectrum. This corresponds to a limit on the transition probability of solar neutrinos to anti-neutrinos of $1.3\times10^{-4}$ (90\% C.L.) for $E_{\bar{\nu}}>1.8$ MeV, covering the entire $^{8}$B spectrum. Best differential limits on anti-neutrino fluxes from unknown sources are also obtained between the detection energy threshold of 1.8 MeV and 17.8 MeV with more than 2 years of data.