Context : Vela X is a region of extended radio emission in the western part of the Vela constellation : one of the nearest pulsar wind nebulae ( PWNe ) , and associated with the energetic Vela pulsar ( PSR B0833-45 ) . Extended very-high-energy ( VHE ) \gamma -ray emission ( HESS \mathrm { J 0835 \mathchar 45 \relax 455 } ) was discovered using the H.E.S.S . experiment in 2004 . The VHE \gamma -ray emission was found to be coincident with a region of X-ray emission discovered with { \it ROSAT } above 1.5 keV ( the so-called Vela X cocoon ) : a filamentary structure extending southwest from the pulsar to the centre of Vela X . Aims : A deeper observation of the entire Vela X nebula region , also including larger offsets from the cocoon , has been performed with H.E.S.S . This re-observation was carried out in order to probe the extent of the non-thermal emission from the Vela X region at TeV energies and to investigate its spectral properties . Methods : In order to increase the sensitivity to the faint \gamma -ray emission from the very extended Vela X region , a multivariate analysis method combining three complementary reconstruction techniques of Cherenkov-shower images is applied for the selection of \gamma -ray events . The analysis is performed with the On/Off background method , which estimates the background from separate observations pointing away from Vela X ; towards regions free of \gamma -ray sources but with comparable observation conditions . Results : The \gamma -ray surface brightness over the large Vela X region reveals that the detection of non-thermal VHE \gamma -ray emission from the PWN HESS \mathrm { J 0835 \mathchar 45 \relax 455 } is statistically significant over a region of radius 1.2 ^ { \circ } around the position \alpha = 08 ^ { \mathrm { h } } 35 ^ { \mathrm { m } } 00 ^ { \mathrm { s } } , \delta = -45 ^ { \circ } 36 ^ { \mathrm { \prime } } 00 ^ { \mathrm { \prime } \mathrm { \prime } } ( J2000 ) . The Vela X region exhibits almost uniform \gamma -ray spectra over its full extent : the differential energy spectrum can be described by a power-law function with a hard spectral index \Gamma = 1.32 \pm 0.06 _ { \mathrm { stat } } \pm 0.12 _ { \mathrm { sys } } and an exponential cutoff at an energy of ( 14.0 \pm 1.6 _ { \mathrm { stat } } \pm 2.6 _ { \mathrm { sys } } ) TeV . Compared to the previous H.E.S.S . observations of Vela X the new analysis confirms the general spatial overlap of the bulk of the VHE \gamma -ray emission with the X-ray cocoon , while its extent and morphology appear more consistent with the ( more extended ) radio emission , contradicting the simple correspondence between VHE \gamma -ray and X-ray emissions . Morphological and spectral results challenge the interpretation of the origin of \gamma -ray emission in the GeV and TeV ranges in the framework of current models . Conclusions :