How can a microorganism adapt to a variety of environmental conditions despite the existence of a limited number of signal transduction mechanisms? We show that for any growing cells whose gene expression fluctuate stochastically, the adaptive cellular state is inevitably selected by noise, even without a specific signal transduction network for it. In general, changes in protein concentration in a cell are given by its synthesis minus dilution and degradation, both of which are proportional to the rate of cell growth. In an adaptive state with a higher growth speed, both terms are large and balanced. Under the presence of noise in gene expression, the adaptive state is less affected by stochasticity since both the synthesis and dilution terms are large, while for a nonadaptive state both the terms are smaller so that cells are easily kicked out of the original state by noise. Hence, escape time from a cellular state and the cellular growth rate are negatively correlated. This leads to a selection of adaptive states with higher growth rates, and model simulations confirm this selection to take place in general. The results suggest a general form of adaptation that has never been brought to light--a process that requires no specific mechanisms for sensory adaptation. The present scheme may help explain a wide range of cellular adaptive responses including the metabolic flux optimization for maximal cell growth.