  A $\theta_{13}$ oscillation analysis based on the observed antineutrino rates
at the Double Chooz far and near detectors for different reactor power
conditions is presented. This approach provides a so far unique simultaneous
determination of $\theta_{13}$ and the total background rates without relying
on any assumptions on the specific background contributions. The analysis
comprises 865 days of data collected in both detectors with at least one
reactor in operation. The oscillation results are enhanced by the use of 24.06
days (12.74 days) of reactor-off data in the far (near) detector. The analysis
considers the \nue interactions up to a visible energy of 8.5 MeV, using the
events at higher energies to build a cosmogenic background model considering
fast-neutrons interactions and $^{9}$Li decays. The
background-model-independent determination of the mixing angle yields
sin$^2(2\theta_{13})=0.094\pm0.017$, being the best-fit total background rates
fully consistent with the cosmogenic background model. A second oscillation
analysis is also performed constraining the total background rates to the
cosmogenic background estimates. While the central value is not significantly
modified due to the consistency between the reactor-off data and the background
estimates, the addition of the background model reduces the uncertainty on
$\theta_{13}$ to 0.015. Along with the oscillation results, the normalization
of the anti-neutrino rate is measured with a precision of 0.86\%, reducing the
1.43\% uncertainty associated to the expectation.
