A 5-year longitudinal study in Great Britain found that moving to a greener area not only improves people's mental health, but that the effect is sustained for a long time. Individuals who moved to greener areas had significantly better mental health in all three post-move years. Those who moved to less green areas suffered a drop in mental health in the year preceding the move but then returned to baseline.
Alcock, Ian, Mathew P. White, Benedict W. Wheeler, Lora E. Fleming, and Michael H. Depledge. (2014). Longitudinal effects on mental health of moving to greener and less green urban areas. Environmental Science & Technology, 48(2), 1247-1255.