The proposal, introduced in April, would have allowed criminal suspects to be extradited to mainland China.
The bill was suspended in June when Lam called it "dead", but she stopped short of withdrawing it.
Full withdrawal is one of the five key demands of protesters, who are also calling for full democratic rights, the BBC reported.
On Monday, Lam was heard on leaked audio tapes blaming herself for igniting Hong Kong's political crisis, and saying it was unforgivable of her to have caused such huge havoc.
The extradition bill quickly drew criticism after being unveiled in April. Opponents said it would undermine Hong Kong's legal freedoms and might be used to intimidate or silence critics of Beijing.
Hong Kong is now in its 14th successive week of demonstrations, and saw fresh violence between police and activists last weekend.
Ahead of Lam's announcement, leading pro-democracy activist Joshua Wong said the withdrawal of the bill would be "too little too late".
In a series of tweets he said all the protesters' demands had to be met.
Demonstrators also want an independent inquiry into alleged police brutality, an amnesty for those arrested and greater political reforms. They also demand that officials stop describing the protests as riots.
Hong Kong was handed back to China in 1997 after more than 150 years of British rule. It has remained semi-autonomous under a "one country, two systems" principle but some fear China is seeking greater control.
( With inputs from IANS )