China and the U.S. are in the final stage of completing a trade deal, with Beijing offering to lower tariffs and other restrictions on American farm, chemical, auto and other products and Washington considering removing most, if not all, sanctions levied against Chinese products since last year.

The agreement is taking shape following February’s talks in Washington, people briefed on the matter on both sides said. They cautioned that hurdles remain, and each side faces possible resistance at home that the terms are too favorable...