RIO DE JANEIRO—Brazil’s Senate voted early Thursday to put President Dilma Rousseff on trial for allegations that she illegally manipulated fiscal accounts, making her the second leader since democracy was restored in 1985 to be forced to step down amid impeachment proceedings.

In a marathon voting session that began the previous day, 55 senators voted to move forward with the impeachment process while 22 voted against. As a result of the outcome, which was widely expected, Ms. Rousseff has to step down immediately to stand...