The cap will be introduced from 1 April and will save consumers in the UK up to £22.7 million a year, the Financial Conduct Authority (FCA) said.
The FCA, which has previously consulted on the issue, is setting a cap which means credit charges cannot be more than the cost of the product.
Currently, in some cases, rent-to-own consumers are paying in total more than four times the retail price of some goods.
Firms will also be required to benchmark prices, including delivery and installation, against the prices charged by three mainstream retailers.
Christopher Woolard, executive director of strategy and competition at the FCA, said: “The actions we are taking today build on our wider work on high-cost credit and will save some of the most vulnerable consumers in the UK millions of pounds.
“This price cap has been designed to target some of the most excessive prices in the rent-to-own market.”
Mr Woolard said a cooker which would normally retail at around £480 to £500 could end up costing more than £1,700 “all in” from a rent-to-own provider. But under the new price cap, rent-to-own customers would see the cost fall by more than £700.
He said other work is also under way to help expand people’s options outside the rent-to-own sector. For example, some credit unions and retailers are working together to offer white goods at reasonable rates of interest.
Discussions have also been taking place with housing associations about upcycling and recycling schemes.
The FCA will be keeping a close eye on rent-to-own firms’ compliance with the new rules and it will review the price cap in 2020. It is prepared to intervene again if further work is needed.
The FCA has previously said rent-to-own customers are some of the most financially vulnerable in society. Only one third are in work, most are on low incomes of between £12,000 and £18,000, and they are likely to have missed a bill payment in the last six months.