Previous studies have explored potential conflicts between ending poverty and limiting global warming by focusing on the carbon emissions linked to the consumption of the world's poorest.Here we instead focus on economic growth as the main driver of poverty alleviation and estimate the emissions associated with the economic growth needed to eradicate poverty. With this framing, eradicating poverty requires not only to increase the consumption of poor people but also the consumption of non-poor people in poor countries. Even in this more pessimistic framing and with historical energy-and carbon-intensity patterns, the global emissions increase associated with eradicating extreme poverty is small, at 2.37 GtCO2e per year or 4.9% of 2019 global emissions, relative to a scenario without poverty alleviation. These additional emissions would not affect materially the climate change challenge for the rest of the world: global energy emissions would need to be reduced by 2.08 GtCO2e per year, instead of 2.0 GtCO2e per year needed in the absence of any progress towards extreme poverty eradication. Lower inequality, higher energy efficiency, and decarbonization of energy can significantly ease this trade-off: assuming the best historical performance in all countries, in part a conservative scenario considering recent progress in green technologies, the additional emissions for poverty eradication in 2050 are reduced by 90%. At the global level, therefore, the need to eradicate extreme poverty cannot be used as a justification for reducing the world's climate ambitions. When trade-offs exist for specific policies or investments, the eradication of extreme poverty can be prioritized with negligible emissions implications. More ambitious poverty targets require more economic growth in more countries which creates more acute trade-offs. The estimated emissions increase in 2050 of eradicating poverty is 7.4 GtCO2e (or 15.3% of 2019 emissions) with the lower-middle-income poverty line at $3.65 per day and 22.1 GtCO2e (or 45.7% of 2019 emissions) with the $6.85 upper-middle-income poverty line. The challenge to align the world's development and climate objectives is not in reconciling extreme poverty alleviation with climate objectives but in providing middle-income standards of living in a sustainable manner.