The facility is powered by a set-top box, which also lets content broadcast over the past 24 hours be replayed, even if recordings were not scheduled.
The service is included in the price of EE's broadband and landline packages.
One expert called the move "hugely significant".
EE TV includes more than 70 Freeview channels, including BBC One, ITV, Channels 4 and 5, Sky News and Al Jazeera.
In addition, it offers apps for YouTube, Daily Motion and Rakuten's subscription TV and movie service Wuaki.tv, among others
The set-top box contains a one terabyte (TB) hard disk, which the firm said could store up to 25 days worth of standard definition content and five days worth of high-definition shows.
Mobile customers of the UK network who did not previously subscribe to another service from the firm but who want EE TV will need to sign up for a broadband package.
The cheapest one on offer is £9.95 a month plus a further £15.75 a month for a required telephone line, all for a minimum of a one-and-a-half year duration.
The company hopes this will provide them an incentive to switch to its service.
"With EE TV, not only can you watch different streams of live and recorded content, on multiple screens simultaneously, but your mobile becomes the remote," said EE's chief executive Olaf Swantee.
"This gives each viewer the chance to watch, queue and view what they want, when they want."
One industry watcher said he expected the firm's competitors to respond in kind.
"It's a logical move from EE and one that's in direct response to BT launching its mobile service next year," said Paolo Pescatore from the consultancy CCS Insight.
"With EE's broadband business posting good quarterly subscriber growth it has a strong subscriber base to cross-sell to, and puts it in a far stronger position than other quad-play providers - Virgin Media and TalkTalk.
"Today's announcement [also] puts the pressure on others to accelerate their own quad-play plans."
However, he added that he believed EE TV needed to offer a better range of content if it wanted to succeed.
"EE has taken a sensible approach with its TV service as it doesn't want to be embroiled in bidding wars for premium content," Mr Pescatore said.
"However given the exclusion of Netflix, EE must strongly consider forging agreements with other key rights owners including BSkyB for its Now TV service.
"The company must also strengthen the range of on-demand services as this is becoming increasingly important to consumers as underlined by Netflix's growth."
EE said its platform would "include an ever growing range of content applications" over time.
Source: BBC News
