The 35 hour a week childcare offer would also be open to all two to four-year-olds.
According to the political party, childcare providers would be 'adequately' funded to deliver the places, with the amount of funding meeting actual costs.
The policy would be funded by tax changes, ensuring that big businesses pay their share and aligning the tax treatment of income from wealth with income from work, says the Lib Dems.
To ensure parents have greater flexibility at work, the party would also require employers to advertise jobs flexibly unless there are 'clear' business reasons why they cannot.
Speaking at the party's launch in Battersea today, Lib Dem leader Jo Swinson will say, 'For so many people, the cost of childcare simply makes returning to work impossible. This hurts our economy and deprives our workforce of a vital pool of talent.
'The choice for parents now is simply not good enough. That is why Liberal Democrats are proposing a transformational change to our economy, by providing working parents with free childcare from when their child is nine months old.
'This will close the gap between the end of paid parental leave and the start of free childcare provision. It will finally give parents more choice about when they return to work and unlock their untapped potential for our economy.'
Shadow education secretary Layla Moran added, 'Liberal Democrats are the only party which is seriously supporting families as they juggle the demands of modern life, working and parenting, by giving them more choice over how they organise their lives and improve social mobility with early years education.
'Childcare costs can be incredibly expensive, and in many cases, people have found that it makes little financial sense to continue working, when so much of their income is going into nursery costs.
'We want to build a brighter future for this country, and that starts with our children, and those in the early stages of parenting, who need far more support than they have been given.'
Responding to the election promise, the Early Years Alliance said that its fears of the election turning into a game of 'oneupmanship' when it comes to "free" childcare are coming to pass.
Chief executive Neil Leitch commented, 'In 2013, Labour pledged 25 hours a week, in 2015 the Conservatives pledged 30 and now we have the Liberal Democrats offering 35. While we welcome the party's recognition that current funding rates are inadequate and further investment into the sector is desperately needed, it's not clear that those who have developed this policy have realised what a huge impact applying this offer to children from nine months will have on the sector.
'If funded childcare is extended down to nine months - above that is understandably likely to be warmly welcomed by parents - providers' ability to cross subsidise will no longer exist. This means that even the promised increase in fees may not be enough to ensure that providers are able to balance the books and remain sustainable in the long-term.'
