This letter presents a combination of searches for Higgs boson pair production using up to 36.1 fb of proton-proton collision data at a centre-of-mass energy TeV recorded with the ATLAS detector at the LHC. The combination is performed using six analyses searching for Higgs boson pairs decaying into the , , , , and final states. Results are presented for non-resonant and resonant Higgs boson pair production modes. The combined observed limit at 95% confidence level on the non-resonant Higgs boson pair production cross-section is 6.9 times the predicted Standard Model cross-section. Limits are also set on the ratio () of the Higgs boson self-coupling to its Standard Model value. This ratio is constrained at 95% confidence level to . In addition, limits are set on the production of narrow scalar resonances and spin-2 Kaluza-Klein Randall-Sundrum gravitons. Exclusion regions are also provided in the parameter space of the habemus Minimal Supersymmetric Standard Model and the Electroweak Singlet Model.