The council forwarded their application to the committee on new admissions, which will take it up on Friday.
Palestinian U.N. envoy Riyad Mansour thanked the council for quickly and unanimously agreeing to act on the Palestinian application.
"We hope this process not to take too long before we see positive action," he told reporters.
Ultimately, the United States has vowed to veto the measure should it receive enough votes in favor of membership.
The U.S. and its partners want the Palestinians and Israelis to restart stalled Mideast peace talks, and an agreement would erase any opposition to Palestinian membership in the U.N.
The Associated Press contributed to this report.