While Terwilliger has not admitted or denied any wrongdoing under the deal, he agreed to pay a $US150,000 ($A193,000) penalty while HAE will pay $400,000.
SEC announced charges against HAE and the CEO last year.
This followed an investigation which found they fraudulently claimed a Colombian exploration concession held between 1 billion and 4 billion barrels of oil reserves and was worth $100 per HAE share even though the company held a "fractional interest" in the licence.
"Terwilliger and Houston American misled investors by wildly exaggerating the extent and nature of their oil and gas holdings," SEC Enforcement Division associate director Gerald Hodgkins said at the time.
"They used a cadre of third parties to publicise and bolster their misleading claims."
