Scalia, 79, died of apparent natural causes at Cibolo Creek Ranch near Marfa, Texas.
Chief Justice John Roberts confirmed the news in a statement.
"He was an extraordinary individual and jurist, admired and treasured by his colleagues," he said. "His passing is a great loss to the Court and the country he so loyally served."
A source told ABC-7 Scalia was not feeling well after dinner on Friday night. His body was found Saturday morning. An El Paso, Texas, priest has been called to Marfa.
An anonymous federal official told MySanAntonio.com there was no evidence of foul play. The U.S. Marshals Service, the FBI and the Presidio County Sheriff's Office were investigating.
Principal Deputy Press Secretary Eric Schultz said President Barack Obama and first lady Michelle Obama were informed of Scalia's death and "extend their deepest condolences" to his family. A full statement was expected later Saturday.
"We mourn his passing and we pray that his successor on the Supreme Court will take his place as a champion for the written Constitution and the Rule of Law. Cecilia [Abbott] and I extend our deepest condolences to his family, and we will keep them in our thoughts and prayers," Abbott said in a longer statement.
Scalia, the longest serving justice on the Supreme Court, was appointed by President Ronald Reagan in 1986. In his 29 years on the nation's highest court, Scalia was known for his strict adherence to the words of the Constitution as they were originally written.
In a speech Scalia gave in 1996 at Catholic University, he described himself as a textualist and originalist.
"The theory of originalism treats a constitution like a statute, and gives it the meaning that its words were understood to bear at the time they were promulgated," he said. "You will sometimes hear it described as the theory of original intent. You will never hear me refer to original intent, because as I say I am first of all a textualist, and secondly an originalist. If you are a textualist, you don't care about the intent, and I don't care if the framers of the Constitution had some secret meaning in mind when they adopted its words. I take the words as they were promulgated to the people of the United States, and what is the fairly understood meaning of those words."
"He was the solid rock who turned away so many attempts to depart from and distort the Constitution," Abbott said.
To that end, Scalia recently wrote the dissenting opinion on Obergefell v. Hodges, in which the Supreme Court ruled a ban on same-sex marriage unconstitutional.
In his dissent, Scalia took issue with the court becoming involved in "this practice of constitutional revision." He disagreed with the way the court's opinion was written and was noted for using some fiery language, as he did the week before in a ruling about the Affordable Care Act.
"What really astounds is the hubris reflected in today's judicial Putsch," Scalia wrote, later adding, "The opinion is couched in a style that is as pretentious as its content is egotistic.
"The stuff contained in today's opinion has to diminish this court's reputation for clear thinking and sober analysis," he said.
Before Reagan selected Scalia for the high court, the justice had been a member of the U.S. Circuit Court of Appeals for the District of Columbia since 1982. He was known as a conservative scholar -- some thought too conservative -- and for his colorful and often humorous use of language on the bench.
In his dissent on King v. Burwell, in which the Supreme Court ruled federal health subsidies under the Affordable Care Act were constitutional, he wrote, "We should start calling this law SCOTUScare." He also called the court's ruling "interpretive jiggery-pokery."
During his time on the lower court, his opinions had been affirmed on appeal in the Supreme Court about 90 percent of the time.
Scalia's death leaves a vacancy on the 9-person Supreme Court and within hours of his death, battle lines had already been drawn on Capitol Hill over who would name his replacement.
Republican presidential candidate Texas Sen. Ted Cruz said on Twitter he would block attempts by Obama to nominate a replacement for Scalia in his waning term.
"Justice Scalia was an American hero. We owe it to him, & the Nation, for the Senate to ensure that the next President names his replacement," he wrote. NPR also reported Cruz and Sen. Mike Lee, R-Utah., sent text messages to other Senators urging them to block an Obama appointee. Senate Majority Leader Mitch McConnell said Scalia's replacement should be named by "the next president."
Sen. Marco Rubio, R-Fla., called Scalia "one of the most consequential Americans in our history" and praised his interpretation of the Constitution. He also touched briefly on Scalia's replacement on the Supreme Court.
"The next president must nominate a justice who continue Justice Scalia's unwavering belief in the founding principals that we hold dear," he said in a statement.
Speaking from the White House, Obama, who appointed Sonia Sotomayor and Elena Kagan to the court, said he plans to name a replacement during his 10 remaining months in office. The challenge would be getting all 46 Senate Democrats and 14 Republicans to push the nomination through.
"I plan to fulfill my constitutional responsibilities to nominate a successor in due time," he said, calling upon the Senate to likewise fulfill its responsibilities and give the chosen nominee a "fair hearing." However, he said "at this moment, we most of all want to think about his family."