The 35-year-old lawyer, who was jailed for perverting the course of justice, becomes the first MP ever to be removed by the recall process, introduced by David Cameron in 2015.
Some 19,261 people signed the petition - 27.64% of those eligible to take part and well above the 10% threshold for a recall.
The successful petition now triggers a by-election in the Peterborough constituency, in which Ms Onasanya is permitted to stand.
Ms Onasanya was first elected to Parliament as a Labour MP by a wafer-thin majority of 607 in 2017.
A year later, she was charged with perverting the course of justice after lying about a speeding offence. She was expelled by Labour after her conviction and served less than four weeks of a three-month prison sentence earlier this year.
Labour said it will move a writ for the by-election on Thursday, paving the way for Peterborough’s voters to select a new MP within weeks.
Nigel Farage said his new Brexit Party will contest the by-election, but a spokesman said no decision had yet been taken on whether he will be the candidate.
The by-election in a city which voted 61% Leave in the 2016 EU referendum potentially offers the former Ukip leader a route to a seat in Parliament after seven unsuccessful attempts.
Mr Farage tweeted: “I can confirm that @brexitparty_uk will fight the Peterborough by-election. We will give it our best shot.”
Labour chairman Ian Lavery said: “Labour campaigned hard for a victory in this recall petition.
“The people of Peterborough clearly agree that Fiona Onasanya is not fit to be their MP and we’re delighted they will now have the chance to vote for a Labour MP in our excellent candidate, Lisa Forbes.”
Conservative parliamentary candidate for Peterborough Paul Bristow said: “The people of Peterborough deserve a better MP who will vote in Parliament to deliver Brexit.”