The Dow Jones finished up 269,48 points, or 1.6%, at 17,409.72.
The S&P 500 rose 35.55 points to 2,036.09, while the tech-heavy Nasdaq climbed 97.42 to 4,691.87.
The rises followed a rebound on European stock markets, with investors hunting for bargains after two sessions of heavy falls.
Shares in JP Morgan Chase were up 3.3%. Bank stocks have been hit particularly hard since the UK's referendum result was announced last week.
Energy shares climbed as oil prices recovered. Chesapeake Energy shares rose 5.4%, while Marathon Oil was 8.2% higher.
Exxon Mobil climbed 2.3%.
Airline stocks also saw a rebound. Delta Airlines was up 3.9%, and American Airlines climbed 5.9%.
On Tuesday, the Commerce Department revised up its estimate of how fast the US economy expanded in the first quarter of 2016.
The agency said gross domestic product increased 1.1% in the quarter, up from an earlier estimate of 0.8%.
(Closed): US shares closed higher on Tuesday, recovering some of the ground lost since the UK voted to leave the European Union.