[en] In two-particle angular correlation measurements, jets give rise to a near-side peak, formed by particles associated to a higher-p_T trigger particle. Measurements of these correlations as a function of pseudorapidity (Δη) and azimuthal (Δφ) differences are used to extract the centrality and p_T dependence of the shape of the near-side peak in the p_T range 1 < p_T < 8 GeV/c in Pb-Pb and pp collisions at √s_NN = 2.76 TeV. A combined fit of the near-side peak and long-range correlations is applied to the data and the peak shape is quantified by the variance of the distributions. And while the width of the peak in the Δφ direction is almost independent of centrality, a significant broadening in the Δη direction is found from peripheral to central collisions. This feature is prominent for the low-p_T region and vanishes above 4 GeV/c. The widths measured in peripheral collisions are equal to those in pp collisions in the Δφ direction and above 3 GeV/c in the Δη direction. Furthermore, for the 10% most central collisions and 1 < p_T,assoc < 2 GeV/c, 1 < p_T,trig < 3 GeV/c, a departure from a Gaussian shape is found: a depletion develops around the center of the peak. Our results are compared to A Multi-Phase Transport (AMPT) model simulation as well as other theoretical calculations indicating that the broadening and the development of the depletion are connected to the strength of radial and longitudinal flow.