More than half of all tropical forests are degraded by human impacts, leaving them threatened with conversion to agricultural plantations and risking substantial biodiversity and carbon losses. Restoration could accelerate recovery of aboveground carbon density (ACD), but adoption of restoration is constrained by cost and uncertainties over effectiveness. We report a long-term comparison of ACD recovery rates between naturally regenerating and actively restored logged tropical forests. Restoration enhanced decadal ACD recovery by more than 50%, from 2.9 to 4.4 megagrams per hectare per year. This magnitude of response, coupled with modal values of restoration costs globally, would require higher carbon prices to justify investment in restoration. However, carbon prices required to fulfill the 2016 Paris climate agreement [$40 to $80 (USD) per tonne carbon dioxide equivalent] would provide an economic justification for tropical forest restoration.