In June 2010, we confirmed the existence of a giant planet in the disk of the young star Beta Pictoris, located between 8 AU and 15 AU from the star. This young planet offers the rare opportunity to monitor a large fraction of the orbit using the imaging technique over a reasonably short timescale. Using the NAOS-CONICA adaptive-optics instrument (NACO) at the Very Large Telescope (VLT), we obtained repeated follow-up images of the Bpic system in the Ks and L' filters at four new epochs in 2010 and 2011. Complementing these data with previous measurements, we conduct a homogeneous analysis, which covers more than eight yrs, to accurately monitor the Bpic b position relative to the star. On the basis of the evolution of the planet's relative position with time, we derive the best-fit orbital solutions for our measurements. More reliable results are found with a Markov-chain Monte Carlo approach. The solutions favor a low-eccentricity orbit e < 0.17, with semi-major axis in the range 8--9 AU corresponding to orbital periods of 17--21 yrs. Our solutions favor a highly inclined solution with a peak around i=88.5+-1.7 deg, and a longitude of ascending node tightly constrained at Omega = -147.5+-1.5 deg. These results indicate that the orbital plane of the planet is likely to be above the midplane of the main disk, and compatible with the warp component of the disk being tilted between 3.5 deg and 4.0 deg. This suggests that the planet plays a key role in the origin of the inner warped-disk morphology of the Bpic disk. Finally, these orbital parameters are consistent with the hypothesis that the planet is responsible for the transit-like event observed in November 1981, and also linked to the cometary activity observed in the Bpic system.