A Freesat spokesman said the rollout will take place "over the coming months". It continues the BBC's experiment into offering its catch-up service via a subscription-free TV service.
The initial trial launched in November 2009 and involved some 300 viewers with the Freesat Humax digital boxes.
Its expansion comes ahead of the planned launch of rival catch-up service ITV Player, which will also be made available on Freesat in the first half of the year.
Emma Scott, managing director of Freesat, said feedback of the trial has been "really positive", and encouraged many people to access the BBC iPlayer service on TV for the first time.
Scott said: "We will be the only TV platform to offer catch-up services from both major broadcasters on a subscription-free basis and without the need to buy new equipment."
Viewers wishing to access the service will need a Freesat HD (Humax) or Freesat+ (Humax) digital box connected to a satellite dish and to a broadband service of at least 1 Mbps.
Freesat's website has detailed instructions about the service and has created a video to assist viewers set up the player.
BBC iPlayer launched on computers on Christmas Day 2007. It is now available on more than 20 devices, including TV services, games consoles and mobile phones, and receives more than 80 million programme requests per month.
The on-demand service allows UK audiences to catch up with BBC content broadcast over the past seven days. Audiences have a choice of streaming or downloading their chosen programme and, with series catch-up, selected programmes are made available for the entire season.
Last year, the BBC's motoring show 'Top Gear' was the most-watched TV programme of the year on the iPlayer.
Last month, the BBC Trust gave its provisional approval for the corporation involvement in the joint industry venture Project Canvas, which aims to bring multiple VoD services to Freeview and Freesat.
The joint project, which counts the BBC, BT, Five, ITV, Channel 4 and TalkTalk as partners, aims to promote a common technology standard that would allow viewers with a broadband connection to watch on-demand services on their TV sets.