Over 200 million people worldwide live outside their country of birth and typically experience large gains in material well-being by moving to where incomes are higher. But effects of migration on subjective well-being are less clear, with some studies suggesting that migrants are miserable in their new locations. Observational studies are potentially biased by the self-selection of migrants so a natural experiment is used to compare successful and unsuccessful applicants to a migration lottery in order to experimentally estimate the impact of migration on objective and subjective well-being. The results show that international migration brings large improvements in objective well-being, in terms of incomes and expenditures. Impacts on subjective well-being are complex, with mental health improving but happiness declining, self-rated welfare rising if viewed retrospectively but static if viewed experimentally, self-rated social respect rising retrospectively but falling experimentally and subjective income adequacy rising. We further show that these changes would not be predicted from cross-sectional regressions on the correlates of subjective well-being in either Tonga or New Zealand. More broadly, our results highlight the difficulties of measuring changes in subjective well-being when reference frames change, as likely occurs with migration.