  We show that double field theory arises from the color-kinematic double copy
of Yang-Mills theory. A precise double copy prescription for the Yang-Mills
action at quadratic and cubic order is provided that yields the double field
theory action in which the duality invariant dilaton has been integrated out.
More precisely, at quadratic order this yields the gauge invariant double field
theory, while at cubic order it yields the cubic double field theory action
subject to a gauge condition that originates from Siegel gauge in string field
theory.
