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All the magnetically charged ultrastatic and spherically symmetric spacetimesolutions in the framework of linear/nonlinear electrodynamics, with anarbitrary electromagnetic Lagrangian density $\mathcal{L}(\mathcal{F})$depending only of the electromagnetic invariant$\mathcal{F}\!=\!F_{\alpha\beta}F^{\alpha\beta}\!/4$, minimally coupled toEinstein-scalar-Gauss-Bonnet gravity [EsGB-$\mathcal{L}(\mathcal{F})$], arefound. We also show that a magnetically charged ultrastatic and sphericallysymmetric EsGB-$\mathcal{L}(\mathcal{F})$ solution with invariant $\mathcal{F}$having a strict global maximum value $\mathcal{F}_{_{0}}$ in the entire domainof the solution, and such that$\mathcal{L}_{_{0}}=\mathcal{L}(\mathcal{F}_{_{0}})>0$, can be interpreted asan ultrastatic wormhole spacetime geometry with throat radius determined by thescalar charge and the quantity $\mathcal{L}_{_{0}}$. We provide some examples,including Maxwell's theory of electrodynamics (linear electrodynamics)$\mathcal{L}_{_{_{\mathrm{LED}}}} \!=\! \mathcal{F}$, producing the magneticdual of the purely electric Ellis-Bronnikov EsGB Maxwell wormhole derived in[P. Ca\~nate, J. Sultana, D. Kazanas, Phys. Rev. D {\bf100}, 064007 (2019)];and the nonlinear electrodynamics (NLED) models given by Born-Infeld$\mathcal{L}_{_{_{\mathrm{BI}}}} \!=\! -4\beta^{2} + 4\beta^{2} \sqrt{ 1 +\mathcal{F}\!/\!(2\beta^{2})~}$, and Euler-Heisenberg in the approximation ofthe weak-field limit $\mathcal{L}_{_{_{\mathrm{EH}}}} \!=\!\mathcal{L}_{_{_{\mathrm{LED}}}} + \gamma \mathcal{F}^{2}\!/2$. With those NLEDmodels, two novel magnetically charged ultrastatic traversable wormholes (EsGBBorn-Infeld and EsGB Euler-Heisenberg wormholes) are presented as exactsolutions without exotic matter in EsGB-$\mathcal{L}(\mathcal{F})$ gravity.

Simple method to generate magnetically charged ultra-static traversable wormholes without exotic matter in Einstein-scalar-Gauss-Bonnet gravity