He died after battling brain cancer, according to the vice president's office.
"Beau Biden was, quite simply, the finest man any of us have ever known," his father wrote in a statement.
Biden had suffered known health problems dating back to 2010, when he experienced a stroke that did not affect his motor skills or speech.
In 2013, Beau Biden was treated at M.D. Anderson Cancer Center in Houston after he became disoriented and weak while on vacation. He was diagnosed with brain cancer, and after undergoing surgery was given a clean bill of health.
The cancer returned this spring and Biden pursued aggressive treatment at Walter Reed National Military Medical Center in Bethesda, Maryland, the vice president's office said. He died Saturday evening, surrounded by his extended family.
Aside from Vice President and Dr. Jill Biden, Beau Biden is survived by his wife, Hallie; two children, Natalie and Hunter; a brother, also named Hunter; and a half-sister, Ashley.
He survived wreck that claimed mother, sister
Throughout his 2010 and 2013 health episodes, Beau Biden continued serving as Delaware's attorney general, a position to which he was first elected in 2006. A Democrat like his father, he served for two terms, and announced in 2014 he wouldn't seek another four years in office as he prepared a run for governor.
Beau Biden is the second of Joe Biden's children to precede their father in death; the vice president's 1-year-old daughter Naomi was killed in a Christmastime car accident in 1972. The crash also took the life of Joe Biden's first wife, Neilia, who was Beau's mother.
Beau Biden was 2 years old when his mother was killed in the crash. He and his younger brother Hunter were injured but survived the accident, which occurred when a truck careened into the car the family was riding in.
Joe Biden was sworn in as senator at his sons' hospital bedside a few weeks later, and according to the 1988 political biography "What It Takes," by Richard Ben Cramer, the first-term lawmaker threw himself headlong into single parenthood.
"Joe was the parent. Period. No confusion," Cramer wrote. "Joe didn't want anybody else raising his kids, thanks. He was there every night, every weekend. They had stories at bedtime, games of catch on the lawn, outings, trips, places to go."
Beau and Hunter encouraged their father to remarry, and in 1977 Jill Jacobs, now Jill Biden, wife of the vice president, became their stepmother.
"My mom came along -- I have two moms now -- who came along in 1977 and rebuilt our family, and helped my dad rebuild our family," Beau Biden told CNN in 2012. "She's an incredible mother."
Beau Biden grew up in Delaware and graduated from the same Catholic high school as his father. He received his undergraduate degree at the University of Pennsylvania and attended law school at Syracuse University.
A prosecutor and a politician
After serving as a prosecutor in the U.S. attorney's office in Philadelphia for nine years, and briefly working in private practice, Biden won his first election for attorney general in 2006 by 13,000 votes. When he was re-elected in 2010, Beau Biden increased his winning margin to 149,000 votes over his Republican competitor.
During his time in office, Biden took aggressive tactics to tamp down on child sex crimes perpetrators, netting 180 convictions. He also went after banks and mortgage lenders for their roles in perpetrating crooked loans.
A captain in the Delaware Army National Guard, Beau Biden was deployed to Iraq for a year in 2008, serving in an administrative post with the 261st Signal Brigade.
As a campaign surrogate when Joe Biden was selected as Barack Obama's running mate, Beau Biden acted as a fierce partisan, criticizing Republican opponents for lacking what he said was his father's tell-it-like-it-is honesty. His 2012 speech at the Democratic National Convention brought his father to tears.
And while Beau Biden chose to pursue the same field as his father -- from whom he inherited a square jaw and folksy patter -- he claimed in 2010 the pair didn't regularly talk politics.
"Most of the drama doesn't come to our dinner table. We talk about what my kids are doing -- his grandkids -- my brother's three kids, my sister, we talk about the family," he told CNN. "Most of the time it's not about politics."
Beau Biden is the first child of a sitting president or vice president to die since Patrick Bouvier Kennedy passed away two days after his birth in 1963.
On Saturday, Vice President Biden said in his statement, "More than his professional accomplishments, Beau measured himself as a husband, father, son and brother. His absolute honor made him a role model for our family. Beau embodied my father's saying that a parent knows success when his child turns out better than he did."
President Obama, writing in a statement, quoted Irish poet William Butler Yeats -- a favorite of the vice president's -- in honoring Beau Biden's life.
Yeats wrote, "I have believed the best of every man. And find that to believe it is enough to make a bad man show him at his best or even a good man swing his lantern higher."
"Beau Biden believed the best of us all," Obama said. "For him, and for his family, we swing our lanterns higher."