Employees at a Google Fiber contractor in Kansas City, Missouri, voted to unionize Friday, becoming the first workers with bargaining rights under the Alphabet Workers Union.

The 10 full-time workers are employed by BDS Connected Solutions through Alphabet and work in a retail store for Google Fiber, the project that provides high-speed internet access to 19 U.S. markets.

In February, workers at the location petitioned the National Labor Relations Board for formal union recognition after Google and BDS didn't voluntarily agree to allow it. Workers told CNBC they faced union-busting efforts leading up to the vote.

The NLRB counted and approved the 9-to-1 vote Friday. It marks the first location of Google workers to unionize under the Alphabet Workers Union, which was created a year ago alongside the Communications Workers of America amid increased tensions between workers and Google leadership.

The Alphabet Workers Union now has more than 800 members in various locations across the company, but otherwise operates through a "minority union" model, meaning it doesn’t have bargaining rights with leadership.

The Kansas City workers do have bargaining rights, however, and the union's ability to obtain negotiating leverage could motivate other groups of workers to pursue their own elections.

"Our campaign faced many efforts to discourage us from exercising our right to a collective voice on the job," Eris Derickson, retail associate at BDS Connected Solutions and Google Fiber, said in a statement Friday. "Yet it was always clear to all of us that together we can positively shape our working conditions to ensure we all have access to the quality pay, benefits and protections we have earned."

"We all enjoy our work with Google Fiber and look forward to sitting at the negotiating table with BDS Connected Solutions to set a new standard for our workplace to improve both worker, customer and company experience," Derickson said.

The Google Fiber unit union drive is part of a broader movement in the tech industry that's slowly gaining momentum. Amazon workers across several locations are trying to unionize, including at a warehouse in Alabama, where they're in the process of voting for the second time on whether to form a union. Employee votes from a separate drive on New York's Staten Island will be counted on Monday.

"We have many contracts with both unionized and non-union suppliers, and respect their employees' right to choose whether or not to join a union," a Google spokesperson told CNBC. "The decision of these contractors to join the Communications Workers of America is a matter between the workers and their employer, BDS Solutions Group."

A spokesperson for BDS Connected Solutions was not immediately available to comment.

Correction: This story has been updated to reflect the correct name of the Alphabet Workers Union in the headline and the correct name of the National Labor Relations Board in a key point.