His sons and ex-wife came to the stadium construction site after a co-worker called and told them White had been killed.
He'd been an elevator installer for 43 years.
"Great guy, would give you the shirt off his back, literally. And he was just a wonderful man. And I just talked to him last night. And we were planning on going to the movies later this week. And, we're just glad I had a chance to talk to him last night," said White's son Jarvis.
White was on the ground floor of an elevator shaft on the east side of the stadium when the accident occurred just before 7 a.m.
According to Cal/OSHA, White was standing on a ladder beneath the elevator counterweight when the counterweight struck him.
Jarvis White said in more than four decades on the job, his father had never been badly hurt.
"You get your little dents and dings but nothing serious. Nothing ever requiring going to the hospital," he said.
Don White worked for the Schindler Elevator Corporation. They released a statement saying they were, "Extremely saddened by the tragic loss of our employee, Donald White... We offer our sincere condolences to Mr. White's family, friends and co-workers."
The 49ers released their own statement, saying, "Our thoughts and prayers are with the family, friends and co-workers affected by this tragedy. The 49ers family has lost a teammate today."
After the accident, all 1,000 workers at the site were sent home so they could grieve.
Levi's Stadium is scheduled to open next year for the start of the 2014 season. At an estimated cost of more than $1.2 billion. The nearly two million square foot stadium will have 68,500 seats. The stadium is set to host Super Bowl 50 in 2016.
ABC7 News reporter Lisa Amin Gulezian contributed to this report.
