The 94.7 percent vote in favor of authorizing a strike gives union leaders the authority to set a strike date. They didn't set a date immediately and gave no indication when they might act.
The results were announced in a memo to pilots from the chairman of the union's executive committee, Lee Moak, and first reported by The Associated Press.
An arbitration panel must decide by April 15 whether to void the pilots' contract. The union has said it will strike if its contract is rejected.
The nation's third largest carrier, which is operating under bankruptcy protection, has said a strike would put it out of business.
Any strike would likely prompt a court challenge by the company, which would almost certainly seek a restraining order. Moak said in an interview the union will "do what is legal."
Moak said that during a special meeting to be held by Wednesday he will ask union leaders to give him sole authority to set a strike date.
He said the union is still open to negotiations, but he insisted the company hasn't been willing to compromise.
"It's problematic when people want to call it negotiations and one side isn't negotiating," Moak told AP.
Company spokesman Bruce Hicks said the vote made public Tuesday will not affect Delta service.
"Together with our pilots and all of our employees we remain focused on our No. 1 priority, which is taking good care of our customers," Hicks said.
He added that the company is committed to seeking a consensual deal with its pilots.
"The panel asked us to work privately and quietly and we're doing everything we can to honor their requests," Hicks said.
Atlanta-based Delta sought approval to reject its contract with its 5,930 pilots so it can impose up to $325 million in long-term pay and benefit cuts, which would include a wage reduction of at least 18 percent.
Delta's pilots previously agreed to $1 billion in annual concessions, including a 32.5 percent wage cut, in a five-year deal in 2004. But Delta, which has imposed pay cuts on other employees, said it needs more from its pilots after filing for bankruptcy protection in September.
So far, there has been little movement toward a long-term deal to replace an interim deal reached in December, though both sides have met at least a handful of times since arbitration hearings in Washington ended March 23, Moak said. The company has offered to reduce its concessions request to $305 million a year if the pilots reach a consensual deal, while the pilots say they have offered $140 million.
Moak said Tuesday that each sides' table positions have not changed.
He told pilots in his memo that the union isn't using its strike threat as a bargaining tactic.
"All too often over the past months, management has attempted to mischaracterize the defense of our contract as posturing, gamesmanship and, most recently, saber-rattling. They are wrong," Moak wrote.
Of the 5,590 pilots who voted on the strike authorization ballot, 5,295 voted in favor, according to the union.
The company says the average earnings of pilots last year who worked the full year was more than $157,000. The union says line pilots made on average $151,000 last year. Both the union figure and company figure exclude management pilots, though the union figure also excludes instructor pilots and certain other pilots.