The centrist MP for Lewisham East, an outspoken critic of Mr Corbyn, is standing down to become London’s deputy mayor for transport.
She is reported to have been “forced out” of her role by hard-left Momentum activists in her constituency.
Ms Alexander, 43, will become the fourth Labour Party MP to resign from Parliament since last year, sparking rumours of a further exodus.
Jamie Reed and Tristram Hunt both gave up their seats last January, while Andy Burnham quit to run for mayor of Greater Manchester months later.
Ms Alexander’s departure will trigger a by-election in her Lewisham East constituency in south London, a safe Labour seat.
The ex-shadow health secretary, who first became an MP in 2010, was one of a large number of Labour frontbenchers who quit roles in Mr Corbyn’s team in 2016.
At the time, she branded his shadow cabinet “inept, unprofessional and shoddy” and said she “hated” being part of the leader’s top team.
Responding to Ms Alexander’s exit from Parliament, Tory chairman Brandon Lewis said Labour was “too divided to deliver on their promises to working people”.
He added: “This also highlights a complete lack of faith in Jeremy Corbyn and his leadership.
“The remaining moderates left within Labour will now rightly be concerned that they are next on Momentum’s list.”
Ms Alexander will replace current deputy mayor Val Shawcross, the office of Mayor Sadiq Khan has announced.
In a statement, she said she was committed to making sure “everyone has access to a high-quality and affordable public transport network”.
She added: “I know Sadiq wants London’s transport system to be the envy of the world and I am looking forward to playing my part in making that happen.”
Mr Khan added: “Londoners can be confident she will ensure we deliver our ambitious plans to transform London’s transport network over the coming years.”
Since quitting the Labour frontbench, Ms Alexander has campaigned against a hard Brexit, tabling a motion to stop Article 50.
Mr Corbyn said: “I would like to thank Heidi Alexander for her service to the people of Lewisham as their MP for the past eight years, and for her work as shadow health secretary.
“I wish Heidi well in her new role as deputy mayor for London in Sadiq Khan’s team, where I know she will put her talents and knowledge to great use for the people of London.”
Ms Alexander secured an overwhelming majority of 21,123 in her Lewisham East constituency at the 2017 general election.