"Tom brings enormous depth and breadth of knowledge and experience to protecting the homeland to our senior White House team," Trump said in a statement.
"He has a handle on the complexity of homeland security, counterterrorism and cybersecurity challenges. He will be an invaluable asset to our administration."
Bossert will focus on domestic threats while "Michael Flynn remains steadfastly focused on international security challenges," Trump said, referring to the previously named national security adviser, a retired lieutenant general.
Following his service under Bush, Bossert has, since 2009, "run his own independent homeland and national security consulting business and served as a senior cybersecurity fellow at the U.S. Atlantic Council," according to the Trump transition team.
Bossert's government experience is extensive: During the time he worked as deputy homeland security adviser to Bush, his duties included serving as a "principle author of the lessons learned report on the Hurricane Katrina response" and he was "deeply involved in the effort to develop the U.S. cybersecurity strategy."
He additionally served as senior director for preparedness policy and director of infrastructure protection policy.
In Tuesday morning's statement, Bossert said, in part,
"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. The internet is a U.S. invention, it should reflect these U.S. values as it continues to transform the future for all nations and all generations."
Bossert earned his J.D. from the George Washington University Law School and his B.A. from the University of Pittsburgh.
Trump remains at his Florida resort, Mar-a-Lago, holding meetings in preparation for his Jan. 20 inauguration.