Opinions are split over whether the Fed will raise its benchmark interest rate for the first time in almost a decade.
Many are speculating that the Fed will hold off and keep borrowing costs cheap. The Fed winds up its two-day meeting on Thursday.
The Dow Jones industrial average gained 228 points, or 1.4 percent, to 16,599 Tuesday.
The Standard & Poor's 500 index climbed 25 points, or 1.3 percent, to 1,978. The Nasdaq composite rose 54 points, or 1.1 percent, to 4,860.
Industrial stocks rose more than the rest of the market. General Electric gained 2 percent.
Bond prices fell. The yield on the 10-year Treasury note rose to 2.28 percent.