"You have become the face of America's resolve," he said.
Biden also praised the 36,000 runners who plan to run the marathon next week, saying they will send a message to terrorists.
"America will never, ever, ever stand down," he said, to loud applause. He added, "We own the finish line."
In Washington, President Barack Obama was observing the anniversary with a private moment of silence at the White House.
"Today, we recognize the incredible courage and leadership of so many Bostonians in the wake of unspeakable tragedy," Obama said in a statement. "And we offer our deepest gratitude to the courageous firefighters, police officers, medical professionals, runners and spectators who, in an instant, displayed the spirit Boston was built on perseverance, freedom and love."
Obama said this year's race, scheduled for Monday, will "show the world the meaning of Boston Strong as a city chooses to run again."
Authorities say two brothers ethnic Chechens who lived in the former Soviet republic of Kyrgyzstan and the Dagestan region of Russia planned and orchestrated the twin bombings near the marathon finish line on April 15, 2013.
Tamerlan Tsarnaev, 26, died following a shootout with police several days after the bombings. Dzhokhar Tsarnaev, 20, has pleaded not guilty to 30 federal charges and is awaiting a trial in which he faces a possible death sentence. Prosecutors say the brothers also killed MIT police Officer Sean Collier several days after the bombings in an attempt to steal his gun.
Prosecutors have said Dzhokhar Tsarnaev left a hand-scrawled confession condemning U.S. actions in Muslim countries on the inside wall of a boat he was found hiding in following the police shootout.
At the tribute, several survivors of the bombing alluded to their injuries, but focused mainly on the strength they've drawn from fellow survivors, first responders, doctors, nurses and strangers who have offered them support.
"We should never have met this way, be we are so grateful for each other," said Patrick Downes, a newlywed who was injured along with his wife. Each lost a left leg below the knee in the bombings.
Downes described "Boston Strong," the slogan coined after the attack, as a movement that symbolizes the city's determination to recover. He called the people who died "our guardian angels."
"We will carry them in our hearts," he said.
Downes said the city on Monday will "show the world what Boston represents."
He added, "For our guardian angels, let them hear us roar."
Adrianne Haslet-Davis, a ballroom dancer who lost her left leg below the knee and has recently returned to performing on a prosthetic leg, said she's learned over the last year that no milestone is too small to celebrate, including walking into a non-handicapped bathroom stall for the first time and "doing a happy dance."
Gov. Deval Patrick spoke of how the attack has drawn people closer.
"There are no strangers here," he repeated throughout his speech.
Carlos Arredondo, the cowboy hat-wearing spectator who was hailed as a hero for helping the wounded after the bombings, said he came to the tribute ceremony to support survivors and their families.
"You can see how the whole community gathered together to support them and remember," Arredondo said.
After the tributes, many of those in attendance walked in the rain to the finish line for a moment of silence that coincided with the time when the bombs went off. Bells rang and a flag was raised by MBTA police Officer Richard Donohue, who was badly injured during a shootout with the bombing suspects.
Earlier in the day, a wreath-laying ceremony drew the families of the three people killed Martin Richard, Krystle Campbell and Lu Lingzi as well as Collier's relatives.