Students who hold jobs at private colleges are now allowed to unionize.

The National Labor Relations Board announced a 3-1 decision Tuesday in favor of Columbia University students who work as teaching or research assistants. This will allow students at Columbia and any other private schools to unionize.

"The majority found no compelling reason to exclude student assistants from" collective bargaining rights, the board said in a statement.

It marks a powerful victory for students across the country who have sought to do the same thing. Students at Manhattan's The New School and Harvard have also sought to organize under the UAW. The UAW is one of the largest industrial unions in the country, but it has also branched out to represent other types of employees, such as government workers, professors and teachers.

Related: Verizon reaches deal with 36,000 striking workers

The Service Employees International Union is working to build unions for student workers at Duke, Northwestern and American, SEIU said in a statement.

Unions already exist at many public universities, which are governed by separate collective bargaining rules that are outside the NLRB's purview. UAW unions cover students at several public schools -- including the University of Massachusetts, the University of California, Cal State, and the University of Washington.

New York University, which is a private school located about 100 blocks from Columbia, voluntarily recognized a student workers' union in 2013. That spurred Columbia graduate students to try to do the same by forming GWC-UAW in 2014.

But Ivy League schools have historically been opposed to having student workers unionize, and Columbia refused to formally recognize the group -- spurring the labor union advocates to petition the NLRB. That measure was denied by the NLRB's regional office, which cited a NLRB ruling from 2004 that denied a similar request from students at Brown University.

Related: Can Donald Trump win ENOUGH union votes?

Tuesday's ruling overturns the 2004 decision.

GWC-UAW plans to hold union elections "as soon as possible," according to a statement.

Olga Brudastova, a research assistant at Columbia, said on a press call that the newly formed union plans to lobby the university on issues ranging from health insurance benefits to maternity leave and sexual harrassment. Brudastova added that some Columbia graduate students workers haven't been getting paid on time.

"Some of us were not paid on time, delayed by two or three months," she said. "This is a practice that can be stopped with a [union negotiated] contract."