At the moment, while consumers can apply for credit on-line, the contract is not complete until the consumer has signed a paper copy of the agreement.
"We are undertaking the biggest shake-up of the consumer credit market for 30 years, making it relevant for today's market," said Sutcliffe. "Enabling consumers to complete credit agreements from the comfort of their own homes is a key part of this modernisation process."
"This new rule will improve consumer choice without removing any consumer protection, and save business time and resources," he added.
Consumers who enter into credit agreements on-line will have a 14-day 'cooling off' period in which they can cancel the agreement. This gives consumers extra time to shop around for the best deals and seek financial advice.
Lenders will still have to send hard copy letters when any charges for missed payments are imposed or the agreement is cancelled.
The announcement follows on from the recent UK implementation of the EU Distance Marketing of Consumer Financial Services Directive, which governs the sale of pensions, mortgages and other products on-line or by telephone, fax or mail.
The Directive sets common standards for the information that must be supplied to consumers of financial services prior to a contract being concluded at a distance.