Lib Dem leader Jo Swinson said she was “delighted” to welcome Wollaston.
“We have worked together for many months to fight to stop Brexit and, as one of the most respected Members of Parliament, she brings real expertise to our team,” Swinson added.
“As the strongest party for Remainers, we will lead the fight to stop Brexit.”
The coup for the Lib Dems follows the party’s success in the Brecon and Radnorshire by-election on August 1, in which Dodds forced out the Tory candidate.
Wollaston struck a blow against Theresa May when she left the Conservatives alongside Heidi Allen and Anna Soubry in February, as the trio helped form the new group of independents.
They criticised the Tories’ “shift to the right” of politics, adding: “The final straw for us has been this Government’s disastrous handling of Brexit.”
Wollaston, who was first elected in Totnes in 2010, is expected to join Ms Swinson in London on Thursday as she makes her first major speech as party leader.