Averting a strike that could have shaken the U.S. economy, the union representing more than 300,000 United Parcel Service employees announced Tuesday that its members had ratified a new labor agreement with the shipping giant.

The union, the International Brotherhood of Teamsters, said that its UPS members approved the five-year contract with more than 86 percent support.

The Teamsters have said that the agreement includes wage gains of at least $7.50 an hour for current employees over its five-year term. It also raises the minimum pay for part-time workers to $21 an hour from under $17, and raises the top rate for full-time delivery drivers to about $49 on average.

Under the previous contract, which expired on Aug. 1, full-time drivers made an average of about $42 an hour after four years on the job.

In a statement, the union’s president, Sean O’Brien, said the contract was the most lucrative ever at UPS and would serve as a model for other workers that the union is seeking to organize. “This is the template for how workers should be paid and protected nationwide, and nonunion companies like Amazon better pay attention,” Mr. O’Brien said.

The Teamsters have made unionizing Amazon a top priority in recent years, and Mr. O’Brien said while running for the union’s presidency in 2021 that doing so would first require big, concrete gains at other companies.

Despite the ratification, the new UPS contract will not take effect immediately. The union said in its statement that a group of workers in Florida voted down a supplement to the national contract that covers about 175 members — one of 44 supplements that the union also negotiated.

The union said its negotiators would immediately meet with UPS to resolve the remaining issues so that those Florida members can vote again. The national contract will take effect once the supplement is approved.

UPS declined to comment beyond a brief news release noting the ratification vote and stating that the Florida supplement would be “finalized shortly.”

The Teamsters had been aggressive in mobilizing members and ratcheting up pressure on the company in recent months, including picket-line practice and training sessions for strike captains. Mr. O’Brien has frequently referred to corporate leaders as a “white-collar crime syndicate” and argued that “this multibillion-dollar corporation has plenty to give American workers — they just don’t want to.”

UPS moves about one-quarter of the tens of millions of packages shipped in the United States each day, according to the Pitney Bowes Parcel Shipping Index. Its adjusted net income rose more than 70 percent from 2019 to last year, reaching more than $11 billion.

The negotiations on a national contract began in April, and the union announced in mid-June that its members had voted overwhelmingly to authorize a strike.

The two sides resolved many key issues by early July, including eliminating a lower-paid category of full-time driver that had angered many UPS employees, and requiring air conditioning in new trucks to improve heat safety. But then negotiations broke down, with the Teamsters arguing that the company had not offered sufficient improvements in pay for part-time workers, who make up more than half of the union’s UPS members.

Mr. O’Brien and the union spent the next few weeks condemning what they sometimes referred to as “part-time poverty” jobs, before the sides resumed negotiating in late July and quickly finalized a tentative deal.

UPS employees represented by the union began voting on the agreement in early August. While some part-time workers continued to argue that the wage gains should have been even larger and urged a “no” vote, the final margin suggested that most were satisfied with the deal.

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