President Trump gave Elon Musk a formal send-off on Friday after one of the most tumultuous experiments in modern American governance, in which the world’s richest man had free rein to slash the federal work force.

After roughly four months leading the Department of Government Efficiency, Mr. Musk ended up with a bruised reputation and a literal black eye, which he blamed on his 5-year-old son punching him in the face.

Mr. Musk said he would turn his focus to his businesses now that his time as a “special government employee” had ended. And while DOGE has not come close to delivering the $1 trillion in savings that Mr. Musk promised, he has racked up significant personal benefit in recent months — including having his allies chosen to run NASA and the Air Force, two key customers for his SpaceX company.

In the Oval Office on Friday, Mr. Trump praised Mr. Musk as “one of the greatest business leaders and innovators the world has ever produced,” and said Mr. Musk would continue to advise the administration on cutting costs.

“The DOGE team will only grow stronger over time,” Mr. Musk said.

Mr. Musk’s chapter in Washington began with a chain saw and a deep well of support among Republican lawmakers and allies eager to assist his effort to root out waste, fraud and abuse in the government. It ended with a cordial joint news conference with Mr. Trump, where Mr. Musk was largely on the sidelines.

Even as the two men grew more distant over the past several months, Mr. Trump still went to great lengths Friday to show there was no animosity between them.