A total of 20,687 members backed the motion and on Friday (AEST) the club revealed that the minimum threshold of 16,250 required to move the process on had been deemed authentic.
Once the final results are submitted and a period of review passes, the board of directors will have between 10 and 20 working days to set a date for the vote.
"Pending the final closure of the validations process, this Wednesday, October 7, the cutoff of the 16,250 valid signatures necessary for the vote to succeed was exceeded," A Barca statement read.
"Once the panel makes the final result official and the vote of no confidence is admitted, a few days will be taken to attend to the resolution and the claims of the census, and then the board of directors will have a period of no less than 10 working days and no more than 20 to call the vote."
Support for the motion intensified in August, when Lionel Messi confirmed his desire to leave Barca in the wake of its 8-2 Champions League quarter-final humiliation at the hands of Bayern Munich.
The club brought forward planned presidential elections to March, but Bartomeu could now be ousted in advance.
Barca vice-president Jordi Cardoner said in a news conference: "Despite the many things that have been said and written, this board is a team. We are all together.
"We are with president Josep Maria Bartomeu in the tough times, as we are going through now. There is uncertainty around at personal level but also in regards to health. We don't know how we will be tomorrow.
"However, more than ever, we have the unity, the effort and the credit, the credit that many memberships gave us. We will individually give our best and we will be responsible until the last day that the president and his board are in charge. That's it."
Messi did not end up leaving Barca, claiming Bartomeu made it "impossible" for him to do so by going back on his word to let him go for free.
However, the six-time Ballon d'Or winner only remains under contract until the end of June.
More questions were raised when the club allowed Luis Suarez to leave for Atletico Madrid and failed to sign a replacement striker before the close of the transfer window.