The nature of b-quark jet hadronisation has been investigated using data taken at the Z peak by the DELPHI detector at LEP. Two complementarymethods are used to reconstruct the energy of weakly decaying b-hadrons, EweakB. The average value of xweakB = EweakB/Ebeam is measured to be 0.699 ± 0.011. The resulting xweakB distribution is then analysed in the framework of two choices for the perturbative contribution (parton shower and Next to Leading Log QCD calculation) in order to extract measurements of the non-perturbative contribution to be used in studies of bhadron production in other experimental environments than LEP. In the parton shower framework, data favour the Lund model ansatz and corresponding values of its parameters have been determined within PYTHIA 6.156 from DELPHI data: a=1.84+0.23-0.21 and b=0.642+0.073-0.063 GeV-2, with a correlation factor ρ=92.2%. Combining the data on the b-quark fragmentation distributions with those obtained at the Z peak by ALEPH, OPAL and SLD, the average value of xweakB is found to be 0.7092 ± 0.0025 and the non-perturbative fragmentation component is extracted. Using the combined distribution, a better determination of the Lund parameters is also obtained: a = 1.48+0.11-0.10 and b = 0.509+0.024-0.023 GeV-2, with a correlation factor ρ 92.6%. © The Author(s) 2011.