Abuja
The protests broke out in recent days after a video circulated last week alleging to show members of the unit - known as SARS - shooting dead a man in Delta state.
It also prompted a globally-trending social media campaign to disband the group.
“The dissolution of SARS is in response to the yearnings of the Nigerian people,” the statement said.
It added that the police was redeploying members of the unit and would announce a new strategy to tackle SARS’ remit of fighting armed robbery, kidnapping and other violent crime.
The unit’s alleged heavy-handed methods have for years drawn condemnation from Nigerians, particularly the young, who say SARS officers regularly target, beat and extort them.
On Sunday, Nigerian police used teargas to disperse hundreds of protesters in the capital Abuja, in a repeat of what witnesses said were similar events on Friday.
Police officials and politicians have said they were disbanding or reforming the group multiple times in recent years, though with little visible change, critics say.
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