Mohamed Nur, 33, of Bond Way, SW8, was charged with murder and possession of an offensive weapon.
He has also been charged with a further count of possession of an offensive weapon and three counts of causing grievous bodily harm against two women and a man.
The two women and a man suffered slash injuries in separate incidents in Town Hall Parade, Brixton Road and Acre Lane in Brixton, that happened within a one-hour period on Saturday, 29 April.