Trump's new department for streamlining authorities is abbreviated Doge, like the meme featuring a dog that is also Musk's favorite cryptocurrency dogecoin's logo.
Musk will lead the work together with the former presidential candidate Vivek Ramaswamy.
"Together, these two wonderful Americans will pave the way for my administration to dismantle the state bureaucracy, cut unnecessary regulations, reduce wasteful spending, and restructure federal authorities", Trump says in a statement.
"Shockwaves"
Musk says they will "send shockwaves through the system, and to everyone involved in state waste".
Doge will, according to Trump, assist the government with advice and guidance, and together with the White House, drive comprehensive structural changes. Trump refers to it as a department, but it is unclear whether it will be subordinate to the government.
The work is to be completed by July 4, 2026, at the latest, according to the statement.
Fox profile becomes Defense Minister
Trump appointed a number of key players in his new government on Tuesday evening.
Fox News profile Pete Hegseth becomes Defense Minister. He is one of the hosts of "Fox & Friends Weekend", where Trump has participated several times. Hegseth has military experience and has served, among other places, in Afghanistan and Iraq.
At the same time, it is clear that South Dakota Governor Kristi Noem is appointed Minister for Homeland Security.
Trump also nominates John Ratcliffe as head of the intelligence agency CIA. He served as the US National Intelligence Director during the last months of Trump's previous term and was previously a member of the House of Representatives for Texas.
Golf partner to the Middle East
Earlier on Tuesday evening, Trump also appointed former Arkansas Governor Mike Huckabee to become the next US ambassador to Israel.
It is also clear that real estate investor Steven Witkoff, Trump's long-time friend and golf partner, becomes a special envoy to the Middle East.
Trump also confirmed the previously tipped appointment of Mike Waltz as National Security Adviser. Waltz, who was re-elected to the House of Representatives last week, is a staunch Trump supporter and is described as having a hawkish stance on China.
