The RBI will also consider the application of India Post, but the central bank said it would done separately in consultation with the government.
This would be the first time in a decade that new banking licences are handed out, since the formation of Yes Bank in 2004.
There were 25 companies in the running. Public sector unit IFCI and private players such as Anil Ambani group and Aditya Birla group were among the applicants. Bajaj Finance, Muthoot Finance, Religare Enterprises and Shriram Capital had also applied.
The approval comes a day after the Election Commission (EC) cleared the decks for RBI to announce approvals for new banking licences.
The RBI had sought permission of the EC before announcing the awardees, as the model code of conduct is in place in the run up to the elections.
The "in-principle" approval granted will be valid for a period of 18 months during which the applicants have to comply with the requirements under the banking licence guidelines and fulfil the other conditions as may be stipulated by the RBI.
On being satisfied that the applicants have complied with the requisite conditions, the RBI would consider granting of a licence for commencement of banking business. Until a regular licence is issued, the applicants would be barred from doing banking business.
In February, the Bimal Jalan panel, which scrutinized applications for new bank licences, submitted its report to RBI.