Mr Marshall-Andrews told The Times he had jumped ship in light of the Brexit campaign and Labour's refusal to stand aside in the Richmond Park by-election.
The QC and barrister was MP for Medway from 1997 to 2010.
A Labour spokesman said: "Bob Marshall-Andrews has not been a member of the Labour Party for some years."
Lib Dem leader Tim Farron said he was "coming over to the only party that is offering a credible opposition to a divisive Tory Brexit government".
Mr Marshall-Andrews used to sit with the socialist group of Labour MPs alongside Mr Corbyn and shadow chancellor John McDonnell.
He pointed to last year's by-election in South West London as a key moment in his decision-making.
That Richmond Park election saw the Conservatives and UKIP stand aside in order to avoid taking votes from Zac Goldsmith, while the Greens refused to put up a candidate to allow the Lib Dems a free run. Labour rejected calls to not put up a candidate.
"Faced with a common enemy on this historic issue there was an urgent requirement for a common strategy if not common sense. Labour rejected both and fielded a candidate," said Mr Marshall-Andrews.

More than 300 people entered Alternative Model of the Year with the winner being decided by judges in Newcastle on Saturday.
Vintage-fan Zoe Waters, 19, from Bishop Auckland, is a student at Newcastle University.
Ms Waters said she was shocked to be declared the winner. "I've always dressed a bit crazy," she said.
"I don't know why I wanted to be different, I guess I just always choose to wear what I like and look how I want to look rather than worrying about what's in fashion."
She said she now plans to pursue a career in modelling.
"I'm only 5ft 3in tall and I never wanted to look normal so I never thought I could actually be a model, I hadn't realised how big the alternative modelling world is."
Organiser Kieran Martin said: "There is a lot of prejudice and hatred for people from sub-cultures so we wanted to create something that would celebrate the different lives we have, we are proud of what we are achieving."
The final was held at Northumbria University in Newcastle.

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Former Labour MP Bob Marshall-Andrews has defected to the Lib Dems after describing Jeremy Corbyn's party as a "political basket case".
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A philosophy student who wears vintage clothing has won a national contest for alternative models.
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Each day we feature a photograph sent in from across England.