This note presents a combination of searches for Higgs boson pair production using 126-139 $\mathrm{fb}^{-1}$ of proton-proton collision data recorded with the ATLAS detector at a center-of-mass energy of $\sqrt{s}=$ 13 TeV at the LHC. Three searches for pairs of Higgs bosons, in the $b\bar{b}\gamma\gamma$, $b\bar{b}\tau^{+}\tau^{-}$, and $b\bar{b}b\bar{b}$ final states, are included in this combination. The non-resonant interpretation uses results from the $b\bar{b}\gamma\gamma$ and $b\bar{b}\tau^{+}\tau^{-}$ searches, while the resonant interpretation uses results from all three searches. No statistically significant excess above the Standard Model expectation has been found. Upper limits are set on the production rate of non-resonant Higgs boson pairs, at the 95\% confidence level, assuming Standard Model kinematics. The observed (expected) combined upper limit is found to be 3.1 (3.1) times the Standard Model prediction. The value of the Higgs boson trilinear self-coupling modifier $\kappa_{\lambda} \equiv \lambda_{HHH}/\lambda_{\mathrm{SM}}$ is excluded outside the observed (expected) range $-1.0 \le \kappa_{\lambda} \le 6.6$ ($-1.2 \le \kappa_{\lambda} \le 7.2$) at 95\% confidence level. Upper limits on the production cross-section of a heavy scalar resonance decaying to two Standard Model Higgs bosons are set at 95\% confidence level between 1.1 and 595 fb (1.2 and 392 fb) in observation (expectation), depending on the resonance mass, $m_X$, within the studied mass range 251 GeV $\le m_X \le$ 3 TeV.

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