Tuesday's memo was signed by all members of the Joint Chiefs of Staff.
There has also been a renewed focus on extremism within the United States military after the Capitol storming.
"The violent riot... was a direct assault on the US Congress, the Capitol building, and our Constitutional process", it said.
Amid worry about renewed violence on Inauguration Day, the military's top leaders issued a written reminder to all service members Tuesday that the deadly insurrection at the Capitol last week was an anti-democratic, criminal act, and that the right to free speech gives no one the right to perpetrate violence.
"We are living through something this country has never, ever lived through before", Hagel told McClatchy in a phone interview.
It's not clear how many current and retired veterans took part in the riot at Capitol, and the full extent of the involvement of military members is under investigation.
The military leaders added that Biden will be inaugurated on January 20 in accordance with the Constitution and become their 46th commander in chief. He and the other members are military advisors to the president, the secretary of defense and the National Security Council.
The Joint Chiefs memo did not allude directly to the question of military involvement.
More than one-third of all active-duty troops and more than half of minority service members say they have personally witnessed examples of white nationalism or ideological-driven racism, according to a 2020 survey of active-duty Military Times readers.
While a number of Trump's cabinet members including acting Defence Secretary Chris Miller condemned the storming, the top United States general, Chairman of the Joint Chiefs of Staff General Mark Milley, was silent until now.
"As we have done throughout our history, the USA military will obey lawful orders from civilian leadership, support civil authorities to protect lives and property, ensure public safety in accordance with the law, and remain fully committed to protecting and defending the Constitution of the United States against all enemies, foreign and domestic", the message, sent out on Tuesday to all troops, reads.
"Any act to disrupt the Constitutional process is not only against our traditions, values, and oath: it is against the law", the message reads.