Mr Trump is accused of inciting a mob that stormed Congress last week after he repeated false claims of election fraud. Five people died.
The trial will be held after the president leaves office next Wednesday.
If Mr Trump is convicted, senators could also vote to bar him from ever holding public office again.
The trial follows Wednesday's vote in the House of Representatives that formally charged - or impeached - the president with "incitement of insurrection" for his role in the riot.
The Republican president has rejected responsibility for the violence. In a video released by the White House after the vote, he called on his supporters to remain peaceful, without mentioning his impeachment.
The FBI has warned of possible armed protests planned for Washington DC and all 50 US state capitals in the days before Joe Biden, a Democrat, is inaugurated as the new US president.