Presidential spokesman Dosaly Esenaliev told RFE/RL that Bakiev signed a decree to that effect on September 13.
Esenaliev has been temporarily replaced by Elmurza Satybaldiev.
Bakiev's office also confirmed that the president had relieved his younger brother, Janysh, of his duties as the SNB's first deputy chairman.
Tabaldiev on September 12 told parliament he had asked to be dismissed after allegations that Janysh Bakiev could be involved in a purported plot to frame opposition leader Omurbek Tekebaev.
Tekebaev was arrested at Warsaw airport last week after Polish border police found heroin in his luggage.
A Polish court later ordered his release, saying it had accepted his claims that the drugs had been planted before he boarded his flight at Bishkek airport.
Janysh Bakiev on September 13 denied being fired. He said that he stepped down voluntarily to help investigators clarify the circumstances that led to Tekebaev's detention.
Kyrgyz lawmakers earlier this week made public a letter purportedly written by the deputy head of Bishkek airport, Nadyr Mamyrov. The letter suggests Janysh Bakiev directly arranged for narcotics to be planted in Tekebaev's luggage.
Mamyrov says the letter was a forgery.