Stalking has become a specific criminal offence in England and Wales in a move to improve victims' safety.
The government has introduced two offences, stalking and stalking involving a fear of violence.
Campaigners had long claimed dealing with stalking under existing harassment laws was inadequate. In Scotland stalking was made an offence in 2010.
A parliamentary inquiry earlier this year found that about 120,000 victims, mostly women, were stalked every year.
However only 53,000 incidents are recorded as crimes by police - and only one in 50 of these reports leads to an offender being jailed.
The inquiry called for a new offence to be introduced at once, saying harassment and intimidation could often turn into murder.
After meeting victims and campaigners at Downing Street earlier this year, the prime minister described stalking as "an abhorrent crime" which "makes life a living hell for the victims".
The new law of stalking carries a maximum six-month sentence and stalking involving a fear of violence or serious distress carries a maximum five years in prison.
BBC legal correspondent Clive Coleman said the government hoped that adding specific offences of stalking would provide greater clarity around the offence for the police and others looking to improve the safety of victims and bring perpetrators to justice.
The calls for reform came after a series of cases involving stalkers who went on to kill, including Clifford Mills, 49, who stalked his ex-girlfriend Lorna Smith on Facebook before stabbing her to death at his flat in Brixton, south London, in February last year.
He was jailed in February for life, with a minimum term of 21 years, after being found guilty of murder.