The BBC’s director general Tony Hall said the aim was to launch the “BritBox” rival to Netflix in the UK the second half of 2019.
The announcement came as ITV reported 2018 profits of £567m, up 13%.
ITV’s chief executive Dame Carolyn McCall said it was an “uncertain economic and political environment”.
She said the “BritBox” rival to Netflix will be the home for the “best of British creativity”.
Neither organisation would say how the services would be priced, but Lord Hall said it would be “competitive”.
There are reports it could cost £5 a month.
The two organisations already have a BritBox streaming service in North America which Lord Hall said was “ahead of expectations”. It has 500,000 subscribers.
“Research with the British public shows that there is a real appetite for a new British streaming service – in addition to their current subscriptions,” he said.
Dame Carolyn told BBC Radio 4’s Today Programme that 43% of all homes which use the Internet are interested in a subscription. For homes which already subscribe to Netflix, she said that increased to half of all homes.
“There is a window of opportunity here,” she said.
ITV will spend £25m on the venture this year and £40m in 2020.
The new venture is not intended to replace the BBC’s iPlayer or the ITV Hub and is expected to have box sets from the BBC and ITV archives with some new commissions.
There will be “one permanent, comprehensive home where anyone in Britain can get all of our library content – both the ITV and BBC library – in one place and they can watch it anytime, anywhere,” she told Today.
Dame Carolyn told the BBC that existing licensing agreements with Netflix will be honoured. For instance, last year, Netflix acquired the rights to the BBC show Bodyguard – from ITV Studios which owns the production company which made the drama.