Smith, 34, was shot after exchanging words with the driver of a Hummer H2 that rear-ended his Mercedes G63 SUV, causing him to strike another vehicle, police said.
Smith was shot multiple times, and his wife, Racquel, also 34, was shot twice in the right leg, according to police. Smith was pronounced dead at the scene, while his wife was taken to a hospital.
Smith's family released a statement Sunday morning.
"On behalf of the Smith family, we are thankful for the outpouring of support and prayers. We ask that you continue to respect the family's privacy as they grieve the loss of a devoted husband, father and friend."
Police said the driver of the Hummer, Cardell Hayes, 28, has been charged with second-degree murder and that the handgun used in the shooting had been recovered.
The Saints also confirmed Smith's death, with Saints owners Tom and Gayle Benson and general manager Mickey Loomis releasing statements.
"Our thoughts and prayers are with Will and his wife Racquel, but more importantly with their children, William, Wynter and Lisa who are suffering and just starting to realize and deal with an unimaginable loss," Tom and Gayle Benson said. "We are devastated and saddened by Will's tragic and preventable death due to a senseless act that will leave a lasting scar on our community forever."
Said Loomis: "Will came to New Orleans 12 years ago and quickly developed both on the field as a player and off the field as a leader to become one of the cornerstones of a team that would go on to win a Super Bowl. In our community he was an important contributor to numerous charitable causes to benefit those in need. Will's contributions to both our franchise and our community as a whole will always be remembered."
Former Saints running back Pierre Thomas was on the scene shortly after the incident and reportedly had been out with Smith and his wife.
Smith was drafted by the Saints with the 18th overall pick in 2004 out of Ohio State. He spent all nine of his seasons with the Saints and last played in 2012. He was a Pro Bowler in 2006 and ranks fourth in Saints history with 67.5 career sacks. He had a career-high 13 during the Saints' 2009 Super Bowl season.
Saints coach Sean Payton, along with some of Smith's former Saints teammates and fellow NFL players, took to Twitter to express their grief: