Senator Robert Menendez of New Jersey told members of his staff on Tuesday that he planned to resign from Congress in late August, bowing to intense pressure from Democratic colleagues who had urged him to step down or risk expulsion from the Senate after his federal bribery conviction.

Mr. Menendez’s decision to quit months before the end of his third term, even as he prepared to appeal the verdict, will likely allow Democrats to avoid a potentially ugly intraparty fight at a highly fraught political moment. New Jersey’s Democratic governor, Philip D. Murphy, is expected to quickly appoint a replacement who would serve until January.

The decision was described by three people familiar with Mr. Menendez’s remarks who were not authorized to discuss them publicly. One of them said he planned to step down Aug. 20 and could announce the decision publicly as soon as Tuesday afternoon.

By waiting until August, Mr. Menendez will ensure that he receives at least another month of his Senate salary and health insurance, crucial lifelines at a time when his finances are crumbling and his wife, Nadine Menendez, is undergoing cancer treatment. His resignation will not immediately affect his federal pension, but the senator stands to lose it under a federal anticorruption law if his conviction is upheld.

The resignation represents the denouement of a turbulent three-decade career in Washington. It began when he was elected to the House in 1992 as a 38-year-old state lawmaker and saw him rise to become one of the most important voices on foreign policy as the chairman of the Senate Foreign Relations Committee.

Though many called for Mr. Menendez’s resignation after his indictment last fall, demands that he step aside intensified quickly after a jury in Manhattan found him guilty of taking bribes and acting as an agent of Egypt.