The S&P 500 jumped 13.18 (0.70 percent) to 1,885.52, its first record close since March 7.
The Dow Jones Industrial Average advanced 74.95 (0.46 percent) to 16,532.61, while the tech-rich Nasdaq Composite Index surged 69.05 (1.64 percent) to 4,268.04.
Art Hogan, chief market strategist at Wunderlich Securities, said investors feel more reassured about the US economy after "better" data, including a report Tuesday from the Institute for Supply Management that showed US manufacturing activity rose in March.
Investors are also heartened by comments from Fed Chair Janet Yellen on Monday that suggest no "abrupt" change to US monetary policy that has been supporting the economy, Hogan said.
Finally, while geopolitical tensions over Ukraine remain high, they have not worsened, Hogan added.
Major winners included biotechnology stocks that were hammered last week, such as Celgene (+5.0 percent) and Gilead Sciences (+3.9 percent).
Technology companies generally did well, including Facebook (+4.0 percent), Google (+1.8 percent) and Dow member Cisco (+3.1 percent).
Nasdaq heavyweight Apple rose 0.9 percent.
US car giants had a mixed day. Ford Motor vaulted 4.6 percent higher after reporting that March sales in the US rose 3.0 percent from a year ago.
But General Motors continued to feel the drag from the scandal over its recall of millions of vehicles due to safety problems. Chief executive Mary Barra faced tough questioning Tuesday before a congressional panel. GM said US sales rose 4.0 percent in March year-over-year; shares dipped 0.2 percent.
News Corp. benefited from a decision by a US judge to dismiss a lawsuit against Rupert Murdoch and other executives that alleged they had withheld key information about the phone hacking scandal in Britain. Shares rose 1.4 percent.
Bond prices fell. The yield on the 10-year US Treasury bond rose to 2.76 percent from 2.73 percent Monday, while the 30-year advanced to 3.60 percent from 3.57 percent. Bond prices and yields move inversely.