At the moment, the process can take up to six days.
The organisation that manages the cheque clearing system said the changes would be phased in from October 2017.
However, it will be the second half of 2018 before all UK banks and building societies are able to offer the faster service.
Under the new arrangements, co-ordinated by the Cheque and Credit Clearing Company, banks will be able to clear cheques by exchanging pictures of them.
At the moment, all cheques have to be physically transported back to the bank that issued them.
Several banks - including Barclays and Lloyds - also allow their customers to pay in cheques via pictures on their banking apps.
However, this can only happen when the cheque is issued by the same bank.
"These changes will put cheques firmly in the 21st century, delivering real and important benefits for the many individuals, charities and businesses that regularly use cheques," said James Radford, chief executive of the Cheque and Credit Clearing Company.
"Not only will cheques clear faster but banks and building societies may offer their customers the option of paying in an image of a cheque rather than the paper cheque itself."
Although cheque use has declined in recent years, there were still 477 million written in the UK last year.
The industry had wanted to phase them out entirely by 2018. However MPs said they should be retained, as many older people in particular relied on them.
Bank customers who pay cheques into their accounts will soon be able to get the money cleared within one working day.