Carney, 59, launched his bid at an event in the western city of Edmonton, casting himself as an outsider who was not part of Trudeau’s unpopular government.
Trudeau announced his resignation this month amid unhappiness among legislators alarmed by the party’s poor polling numbers ahead of an election this year.
Trudeau, who took office in November 2015, will stay on until his replacement is named on March 9.
Carney’s main rival looks to be former finance minister Chrystia Freeland, whose resignation last month over policy differences led to Trudeau’s decision to quit.
The new prime minister is unlikely to be in office for long. The minority government could be toppled in parliament as soon as the end of March, triggering an election that polls indicate the official opposition Conservatives will win.
Carney, who was also governor of the Bank of England, is running as an outsider with considerable financial experience.
“I am going to be completely focused on getting our economy back on track,” he said during his launch speech.
“I’ve helped manage multiple crises, and I’ve helped save two economies. I know how business works, and I know how to make it work for you.”
That said, he has close ties to Trudeau, who last September named him as chair of a task force on economic growth.
The Conservatives say there is little difference between Carney and Trudeau.
“As a long-time Liberal insider, advisor at least as early as 2020 … Carney is the furthest thing possible from an outsider,” the Conservatives said in a statement on Thursday.
Carney worked for Goldman Sachs before joining the Canadian finance ministry in 2004. He was named Bank of Canada governor in 2007 and quickly had to deal with the after-effects of the global crisis in 2008.
In 2013 he took over as governor of the Bank of England, becoming the first person to ever head two major central banks.
After leaving the bank in 2020, he was appointed UN special envoy for climate action and finance. He was also a senior executive at Brookfield Asset Management and on the board of companies including bond investor PIMCO and fintech giant Stripe.
Carney said he had resigned as the UN special envoy and left all commercial posts before launching his Liberal Party leadership bid.
“I resigned all my roles … cut all my ties. I am all in,” he said.