Major depression is hypothesized to be associated with dysregulations of the hypothalamic–pituitary–adrenal (HPA) axis and impairments in adult hippocampal neurogenesis. Adult-born hippocampal neurons are required for several effects of antidepressants and increasing the rate of adult hippocampal neurogenesis (AHN) before exposure to chronic corticosterone is sufficient to protect against its harmful effects on behavior. However, it is an open question if increasing AHN after the onset of chronic stress exposure would be able to rescue behavioral deficits and which mechanisms might be involved in recovery. We investigated this question by using a 10-week unpredictable chronic mild stress (UCMS) model on a transgenic mouse line (iBax mice), in which the pro-apoptotic gene Bax can be inducibly ablated in neural stem cells following Tamoxifen injection, therefore enhancing the survival of newborn neurons in the adult brain. We did not observe any effect of our treatment in non-stress conditions, but we did find that increasing AHN after 2 weeks of UCMS is sufficient to counteract the effects of UCMS on certain behaviors (splash test and changes in coat state) and endocrine levels and thus to display some antidepressant-like effects. We observed that increasing AHN lowered the elevated basal corticosterone levels in mice exposed to UCMS. This was accompanied by a tamoxifen-induced reversal of the lack of stress-induced decrease in neuronal activation in the anteromedial division of the bed nucleus of the stria terminalis (BSTMA) after intrahippocampal dexamethasone infusion, pointing to a possible mechanism through which adult-born neurons might have exerted their effects. Our results contribute to the neurogenesis hypothesis of depression by suggesting that increasing AHN may be beneficial not just before, but also after exposure to stress by counteracting several of its effects, in part through regulating the HPA axis.