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.
Former Labour MP Bob Marshall-Andrews has defected to the Lib Dems after describing Jeremy Corbyn's party as a "political basket case".