Members gathered at the Spanish and European champions' general assembly voted 697 in favour of the record five-year deal, the biggest for any football club, with 76 against and 36 blank votes, the club said on their website.
Barca President Sandro Rosell and his board of directors had been lobbying members to vote in favour of the agreement amid criticism the club was compromising its ideals by taking money from an unsavoury regime.
Rosell, starting his second season in charge, has argued that the money is needed to help improve the club's financial situation and help pay for the development of its sports teams.
"I would like things to be different and that the Barca shirt could be blank," Rosell said. "But it can't be because that way our opponents would overwhelm us."
The Spanish and European champions were one of the few sides in world football not to have a corporate logo on their shirts, instead displaying the name of the United Nations Children's Fund (UNICEF), for which they paid the organisation 1.5 million euros a year.
Their shirts now carry the name "Qatar Foundation" on the front, with UNICEF relocated to the back below the player's name.
Some members spoke out against the deal, pointing to what they said was Qatar's poor human rights record.
"We want an explanation as to what this deal means," member Marc Ferrer was quoted as saying in Sport newspaper. "I urge reflexion. Vote no so that a dictatorship does not become Barca's sponsor."
Vice President Javier Faus said the cash from Qatar was needed so Barca could live up to its motto of "More than a club".
"It is true that Qatar does not treat its immigrants well. It's not much different to what happens here. They [Qatar] are aware of it and are working on it."
Members also approved the club's accounts for the 2010/11 season and the projected budget for the current season.
Barca made a loss of 9.3 million euros last term, less than half the 24.1 million originally expected, while revenue rose 14 percent to a record 473 million euros.
A net profit of 20.1 million euros has been budgeted for the current season, with income projected at 461 million euros. However, if Barca were to defend their Champions League title, revenue would climb to 491 million, the club said.
Barca are one of four Spanish top-flight clubs which is owned by its members, along with Real Madrid, Athletic Bilbao and Osasuna.
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