Former national security adviser Michael Flynn, who pleaded guilty last week to lying to the FBI about his conversation with a Russian diplomat, told an American businessman that U.S. sanctions on Russia would be “ripped up” under the Trump administration, a whistleblower told a congressman.

Mr. Flynn sent a text message to a former colleague on Inauguration Day saying a nuclear-power project they were both once involved in was now “good to go,” according to the person who was described as a whistleblower in a letter Wednesday...