Mr Farron, who made the announcement at a charity that supports refugees in Gloucestershire, said the UK must show the same moral leadership over Syria as it did when taking in survivors of Nazi concentration camps in 1945.
The estimated £4.3 billion cost of the initiative will be paid back over time by the taxes of those settling in Britain.
He said the UK had taken a “pitiful number of people” from the conflict zone, and had only done so after the government was put under “extreme pressure”.
“This is Britain doing what Britain always should have done in being a place of sanctuary,” Mr Farron said.
“For all that we focus on Brexit, and lots of other things as well, the biggest humanitarian crisis facing our continent is still going on and Britain is turning its back and pretending it’s not happening.”
Iman Nabout, who fled Syria with her husband and two children, cried as she told Mr Farron how thankful she was to be in the UK.
The Lib Dems also pledged to reopen the Dubs scheme to settle lone child refugees. Mr Farron urged the Government to put more resources into teaching new arrivals English so they could find work and contribute to society.
The current government aims to take in 20,000 refugees from Syria by the end of the decade.