The Labour politician received more than 50 per cent of votes in the fourth ballot of MPs, defeating his party colleague Chris Bryant.
Sir Lindsay, formerly a deputy to Mr Bercow, received 325 votes to Mr Bryant's 213.
Speakers must be politically impartial, meaning Sir Lindsay will be required to resign from the Labour Party in order to carry out his duties.
Before leaving Mr Bercow, whose role was supposedly politically neutral, was under fire for a series of controversial rulings widely considered to favour Remain supporters.
Labour's Meg Hillier and Conservative Sir Edward Leigh were eliminated in the first round, and Doncaster Central MP Dame Rosie Winterton was knocked out in the second round - with her Labour colleague Harriet Harman also withdrawing.
Earlier Sir Lindsay highlighted his experience as a deputy speaker for nine years and stressed the need to allow backbench MPs to hold those in power to account.
Sir Lindsay also said the Commons is "not a club" where length of service takes priority, adding: "The person who walked through that door yesterday is just as important to their constituents - their voice must be heard as well - and the pecking order ought not to be there, it is about equality."
Sir Lindsay also vowed to push on with security reforms to keep MPs, their families, staff and the Commons safe.