The regulations aim to tackle firms that cold call people at home when a homeowner has asked not to be contacted.
They should also help authorities tackle companies that send unsolicited text messages to people.
Authorities previously had to prove that someone had suffered substantial damage or distress before a fine could be imposed.
Now the Information Commissioners Office (ICO) will just have to prove that a company has broken the law.
Information Commissioner Christopher Graham said: “We’ve been pushing for this change for two years and we’re sure it will make a difference.
“The change will help us make more fines stick and more fines should prove a real deterrent to the people making these calls.”
He said it was important to note that the ICO will only be able to fine people for serious breaches of the law after the rules change.
“So we can’t fine companies for something they did last week,” he added.
The ICO received 175,000 reports of nuisance calls and texts last year.
The new law allows companies to make marketing phone calls without prior permission, but they must first check with the Telephone Preference Service to make sure the person they are calling has not opted out.
To send a marketing text message they must have permission and must always give details of how people can opt out of any future messages.
Mr Graham appealed for people to get in touch if they fall victim to unwanted calls or texts.
Executive director of Which? magazine Richard Lloyd: “Unwanted calls disrupt the lives of millions every day, so it’s good news it’s now easier for regulators to prosecute nuisance callers.
“Regulators must send a crystal clear message to firms that nuisance calling is unacceptable by using these new powers to maximum effect.”