The party wants to increase the premium, which gives extra funding to early years settings when they take on three- or four-year-olds from disadvantaged backgrounds, from £302 to £1,000.
The increase will cost an extra £70m in 2018/2019, rising to £112m in 2021/22, according to a cost analysis published alongside the manifesto.
Tripling the early years pupil premium was previously a commitment in the Liberal Democrats' 2015 election manifesto. Last November the Social Mobility Commission, in its annual State of the Nation report, called for a doublng of the premium to combat worsening life chances for children and young people.
In addition, the Liberal Democrats have pledged to protect the school pupil premium, which is for children who are eligible for free school meals and is currently set at £1,320 for primary-age pupils and £935 for secondary-age pupils. Schools also receive £1,900 for pupils with experience of the care system.
Early years leaders have backed the party's pledge to bring the value of early years premium more in line with the pupil premium.
"We have long argued that the disparity between the early years pupil premium and primary school pupil premium is unfair and unjustifiable," said Neil Leitch, chief executive of the Pre-school Learning Alliance.
"As such, the pledge to triple the value of the early years pupil premium is very welcome.
"Supporting children from more disadvantaged backgrounds is a vital part of early years provision, and clearly providers are limited in what they can do with £300 per child per year."
Purnima Tanuku, chief executive of National Day Nurseries Association, said: "Currently, the early years sector lags well behind the amount of funding invested in schools. This measure pledged by the Liberal Democrats would bring early years more in line with the amount of early years pupil premium given to schools.
"This is particularly important if more nurseries are to offer funded places to disadvantaged two-year-olds.
"In tripling the early years pupil premium it would recognise the importance of investing in a child's first few years which are key to improving their life chances and reducing inequalities between peers."
The Liberal Democrats' commitments around the pupil premium are part of a wider package of measures for children and young people in their manifesto.
The party has also said it will provide free school meals for all primary school children. The party also wants to lower the voting age to 16, double the number of businesses taking on apprenticeships, and introduce a discount bus pass for all 16- to 21-year-olds, offering two thirds off local ticket prices.
Other pledges include restoring housing benefit for 18- to 21-year-olds and an investment of £7bn in schools and colleges.
Liberal Democrat leader Tim Farron said: "We want to give all our children a brighter future in a fairer Britain where people are decent to each other, with good schools and hospitals, a clean environment and an innovative economy. Not Theresa May's cold, mean-spirited Britain."