The committed Christian bowed out in a surprise statement after facing heavy criticism over his views on homosexuality during the general election campaign.
He faced anger after having to be asked several times before he would say gay sex was not a sin.
Hours before he quit, Lib Dem peer Brian Paddick – who was Britain’s most senior openly gay police officer in the Met Police – piled on pressure by resigning as home affairs spokesman over his “views”.
In a speech to staff at the Lib Dems’ London HQ, Mr Farron declared: “I have found myself torn between living as a faithful Christian and serving as a political leader.
“A better, wiser person than me may have been able to deal with this more successfully, to have remained faithful to Christ while leading a political party in the current environment.”
Workers at Lib Dem HQ received an email urgently summoning them to an emergency meeting at 6pm.
Party officials thought they were being called to a leaving speech for Mr Farron’s longstanding press aide Paul Butters, who resigned earlier this week.
Instead, they were given the bombshell news that their leader was stepping down.
Flanked by party grandees including Vince Cable and Norman Lamb, Mr Farron said journalists “have every right to ask what they see fit”.
But he added: “To be a political leader – especially of a progressive, liberal party in 2017 – and to live as a committed Christian, to hold faithfully to the Bible’s teaching, has felt impossible for me.
“I’m a liberal to my fingertips, and that liberalism means that I am passionate about defending the rights and liberties of people who believe different things to me.
“There are Christians in politics who take the view they should impose the tenets of their faith on society.
“But I have not taken that approach because I fundamentally disagree with it. It’s not liberal and actually it’s counter-productive when it comes to advancing the gospel.
“Even so I seem to have been the subject of suspicion because of what I believe and who my faith is in.
“In which case we are kidding ourselves if we think we yet live in a tolerant liberal society.”