The Dow Jones Industrial Average was up 122.42 points, or 0.47 percent, to 26,201.04. The S&P 500 rose 23.02 points, or 0.80 percent, to 2,910.63. The Nasdaq Composite Index went up 87.02 points, or 1.12 percent, to 7,872.27.
Market expectations for a rate cut in October jumped to 90.3 percent from 77 percent on Wednesday.
Analysts said increasing expectations for rate cuts came after weak economic data.
The Institute for Supply Management (ISM) said Thursday its reading on the U.S. services sector fell last month to its lowest level since August 2016.
The non-manufacturing index registered 52.6 percent, 3.8 percentage points below the August reading of 56.4 percent, according to ISM's report. The figure was also lower than the estimated reading of 55.3 from economists surveyed by Dow Jones.
Respondents are mostly concerned about tariffs, labor resources and the direction of the economy, according to ISM.
Washington said Wednesday that it plans to impose tariffs on a wide range of goods from the European Union (EU) after the World Trade Organization (WTO) gave it permission to levy tariffs on 7.5 billion U.S. dollars of EU exports to counteract subsidies to Airbus.