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We show that to cubic order double field theory is encoded in Yang-Mills theory. To this end we use algebraic structures from string field theory as follows: The L ∞ -algebra of Yang-Mills theory is the tensor product K ⊗ g of the Lie algebra g of the gauge group and a 'kinematic algebra' K that is a C ∞ -algebra. This structure induces a cubic truncation of an L ∞ -algebra on the subspace of level-matched states of the tensor product K⊗ K of two copies of the kinematic algebra. This L ∞ -algebra encodes double field theory. More precisely, this construction relies on a particular form of the Yang-Mills L ∞ -algebra following from string field theory or from the quantization of a suitable worldline theory.