Currently, users can only watch programmes from iPlayer by streaming them on the mobile app, which requires a Wi-Fi or 3G connection, as well as consuming mobile data.
Programmes will be available for up to 30-days after they have been downloaded, or within seven days of being watched.
Users can have the option of downloading multiple programmes, depending on the storage size of their device.
The service is currently only available on Apple devices. The BBC said it will roll it out to Android devices "soon" but has not given an indication of timings.
According to the BBC 30 million mobile requests for iPlayer are made per month, which has surged 142% over the past 12 months.
The BBC rolled out iPlayer for the iPad in February last year. It claims it is now the second most popular way to watch the iPlayer, after the PC.
This move could have an impact on consumers' expectations of rival video on demand services from commercial broadcasters such as ITV, Channel 4 and Five.Follow @shearmans