Forget Brooklyn and San Francisco. Millennials and plenty of others seeking a lower cost of living are pouring into the Western mountain states, boosting economic growth and pushing up apartment rents.

Income from rental apartment buildings nearly doubled between 2004 and 2018 in the eight mountain states, according to a new report from Trepp LLC. The research data firm looked at properties in Arizona, Colorado, Idaho, Montana, New Mexico, Nevada, Utah and Wyoming.

That...