The transverse momentum (p_T) spectra and elliptic flow coefficient (v₂) of deuterons and anti-deuterons at mid-rapidity (| y| < 0.5) are measured with the ALICE detector at the LHC in Pb–Pb collisions at sNN = 2.76 TeV. The measurement of the p_Tspectra of (anti-)deuterons is done up to 8 GeV/ c in 0–10% centrality class and up to 6 GeV/ c in 10–20% and 20–40% centrality classes. The v₂is measured in the 0.8 < p_T<5 GeV/ c interval and in six different centrality intervals (0–5, 5–10, 10–20, 20–30, 30–40 and 40–50%) using the scalar product technique. Measured π^±, K^± and p+p ¯ transverse-momentum spectra and v₂are used to predict the deuteron p_Tspectra and v₂within the Blast-Wave model. The predictions are able to reproduce the v₂ coefficient in the measured p_Trange and the transverse-momentum spectra for p_T> 1.8 GeV/ c within the experimental uncertainties. The measurement of the coalescence parameter B₂is performed, showing a p_T dependence in contrast with the simplest coalescence model, which fails to reproduce also the measured v₂ coefficient. In addition, the coalescence parameter B₂ and the elliptic flow coefficient in the 20–40% centrality interval are compared with the AMPT model which is able, in its version without string melting, to reproduce the measured v₂(p_T) and the B₂(p_T) trend.