Bill Johnson, president of Machinists District Lodge 751, called the proposal "the best contract in the aerospace industry."
Boeing had presented a final contract offer to its largest employees union early Saturday morning, after agreeing to withdraw two of its most contentious proposals.
Contract talks had continued beyond an informal deadline.
The aviation giant pulled back on plans to move to a flexible seven-day work week that would have cut overtime pay for weekend work. Boeing is also took back a plan to have workers begin paying for some of their own health insurance.
"We listened to our employees," Calhoun said. "We had a live call center in the last couple of weeks. We listened to call-in reports every day, and in response to what our employees were telling us ... we withdrew that proposal."
Calhoun said Boeing also promised that no employees would be laid off because of subcontracting - another major sticking point with negotiators - for the International Association of Machinists and Aerospace Workers union, representing about 44,000 Boeing workers.
The 44-month contract proposal includes wage increases of four percent in the first two years and three percent after that, Calhoun said. The average machinist at Boeing earns $40,000 a year, not counting benefits or overtime.
Workers were scheduled to vote on the contract Wednesday. A majority vote in favor would ratify it, while a two-thirds majority would be required to authorize a strike. The current contract expires at midnight Wednesday.
Union negotiators continued to examine the proposal early Saturday morning, Machinists spokesman Tim Flynn said.
The final plan was delivered after a night of negotiations that moved past a preliminary deadline.