"The president is grateful for Tom's commitment to the safety and security of our great country, " said Sanders.
Ms Hicks said she wanted to explore other opportunities, having also worked as Mr Trump's aide during his 2016 presidential campaign.
The arrival of John Bolton as the new national security adviser on Monday triggered the decision to remove Bossert.
It is unclear whether Bossert's resignation was linked to a difference of opinion with Trump on Syria.
So far this year, the president has changed his secretary of state, national security adviser, veterans affairs secretary, Central Intelligence Agency director, chief economic adviser, staff secretary, communications director and members of his legal team.
Cyber experts have listed Bossert among a handful of sober cyber and national security advisers steering the Trump administration, which is lighter on government experience and expertise than its predecessors.
The position of White House national security adviser does not require Senate confirmation.
Bossert, who advised the president on terrorism, cybersecurity, and natural-disaster response, has been a stalwart defender of Trump over the past 15 months. Mr Bolton, Mr Wright said, "distrusts career officials". Jacobs reported that Bolton unexpectedly asked for Bossert's resignation.
"I frankly have a whole lot more confidence that no voter in this country was influenced by those ads", he said. Bolton served as USA permanent representative to the United Nations from 2005 to 2006, and as undersecretary of state for arms control and worldwide security from 2001 to 2005.
He was a Trump favorite for his articulate TV style when defending the administration's agenda and made a name for himself as the public face of the administration's response to hurricanes that hit Texas, Florida and Puerto Rico previous year.