Named after chef Claudia Lawrence (pictured below), who vanished without a trace a decade ago, Claudia's Law came into force on Wednesday.
Police believe the 35-year-old from York - who has not been seen since March 18 2009 - was murdered but her body has never been found.
Her father Peter Lawrence, a churchgoer from York, said "several hundred families" were "queuing up" to make use of the legislation known as the Guardianship (Missing Person's) Act 2017.
Under the law, families can apply to the High Court for guardianship of the affairs of a missing person after they have disappeared for 90 days or longer.
It will mean they can handle everyday financial matters such as making mortgage payments and suspending direct debits for bills.
Operated by the Office of the Public Guardian, families will be able to make use of the scheme for up to four years before having the option of renewing the legal status.
Previously, families could only take over the financial affairs of a missing person if they were declared dead.
Mr Lawrence, who has campaigned for change ever since his daughter's disappearance and was made an OBE for his efforts, said: "It's taken an awful long time but the important thing is it's now here.
"When people are at their lowest emotional ebb, they suddenly find that they can't deal with all these financial and practical things. Well, now that's over.
"There are several hundred families queuing up to deal with this and the Government reckon there might be about 50 applications to the court a year after that.
"It's really important and thank God it's here.
"Claudia is still missing. Obviously the fact we don't know what's happened to her is distressing. Let's hope for everybody else's sakes that they are able to deal with their families' affairs."
Susannah Drury, director of policy and research at the charity Missing People, branded the law a "triumph" for campaigners, adding: "This regulation will mean that families who face the emotional distress of a disappearance will not be blocked from handling the financial and legal affairs of their loved ones."
Advice on applying for guardianship will be available through the charity, Mr Lawrence said.
A Ministry of Justice spokeswoman said: "Coping with the tragedy of a loved one going missing can cause immense pain and stress.
"Claudia's Law, campaigned for so tirelessly by Peter Lawrence, will mean that from today families can manage their loved one's affairs in their absence - removing an enormous burden at such a distressing time."
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