Party leader Jo Swinson said the proposal would close the gap between the end of paid parental leave and the start of free childcare provision.
The Lib Dems have also pledged to provide every child aged two to four with 35 hours of free childcare for 48 weeks of the year.
This would be extended to children aged between nine and 24 months where their parents are in work.
Ms Swinson, who will launch the policy at a rally in Battersea on Saturday, said:
“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 9 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.
“This is part of our bold plan to build a brighter future and fundamentally reshape our economy.”
The party estimates the plan would cost £14.6 billion a year, which would be funded by reversing cuts to corporation tax and increasing capital gains tax.
The announcement comes as Labour vowed to expand free childcare provision to offer 30 hours per week of free care to all children aged between two and four.
Currently, parents of three- to four-year-olds are entitled to 15 hours per week of free childcare, with 30 hours available to those meeting strict criteria.