WASHINGTON--President Donald Trump accelerated his ambitious bid to roll back financial regulation Tuesday, signing into law a measure killing a Securities and Exchange Commission rule aimed at weeding out corruption in the energy industry.

The rule in question is a requirement of the 2010 Dodd-Frank financial overhaul, and was completed in the final months of former President Barack Obama’s administration. It requires energy companies to disclose publicly their payments to governments for the rights to extract oil, gas and...