In the statement, Mr. Trump called Mr. Bossert “an invaluable asset” and praised the breadth of experience he would bring to the new administration. “He has a handle on the complexity of homeland security, counterterrorism and cybersecurity challenges,” Mr. Trump said.

Mr. Bossert served as deputy homeland security adviser for Mr. Bush, and he runs a risk management consulting firm in Washington. He is also a senior fellow at the Atlantic Council, working on the research institution’s Cyber Statecraft Initiative.

Helping to protect the country from cybercrimes is likely to be a major focus for Mr. Bossert in light of the hacking of the Democratic National Committee and other incidents in recent years. Mr. Bossert will face the challenge of balancing cybersecurity needs against the privacy concerns of internet companies.

“We must work toward cyber doctrine that reflects the wisdom of free markets, private competition and the important but limited role of government in establishing and enforcing the rule of law, honoring the rights of personal property, the benefits of free and fair trade, and the fundamental principles of liberty,” Mr. Bossert said in the statement announcing his appointment.

News of Mr. Bossert’s selection drew praise from some members of Congress and former colleagues in the Bush administration, who described him as capable and knowledgeable about threats to the country.