South Wimbledon and Queensway stations will be the first to see their staff moved from ticket offices into ticket halls and on to platforms.
Transport for London (TfL) said it would save £50m annually as it tries to save £4.2bn by 2020.
But Manuel Cortes, from the TSSA union, said London Mayor Boris Johnson was "rushing through" the closures.
Mr Cortes, leader of the Transport Salaried Staffs Association said: "Talks on the safety implications of closing over 250 stations have not even been concluded.
"The mayor doesn't seem concerned about how millions of tourists will cope with fewer staff to help them on their way."
TfL said all stations would remain staffed and 150 new ticket machines would be installed by April 2016.
It added that new visitor centres would be created at larger stations such as Victoria and King's Cross to help visitors.
Nick Brown, London Underground's chief operating officer, said more staff were being placed "where they can offer the best possible assistance" as only 3% of Tube tickets were bought at ticket offices.
He said: "This forms part of our wider vision for the Tube, which includes a 24-hour weekend service on core parts of the network."
But the changes have led to previous strikes by the Aslef and RMT unions.
Labour's London Assembly transport spokeswoman Val Shawcross said: "When he was elected, Boris Johnson promised Londoners he would protect the capital's ticket offices, but today he starts the process of dismantling each and every one of them.
"Whilst there is obviously a big role for ticket machines to play, there is no substitute for a member of staff."
London Underground said after 100 meetings with unions the number of roles to be reduced had fallen from 950 to 897 with no member of staff facing compulsory redundancy or losing money.

Roger Hamer, died from head injuries, a month after the accident on Bury New Road, Ramsbottom, in March 2016.
The Rochdale Coroner's Court jury's narrative verdict found "inconsistencies" in the way Bury Council dealt with some road repairs.
Lessons had been learned and the road would be resurfaced, the council said.
Catherine James, of solicitors Irwin Mitchell, said legal action had started by Mr Hamer's family against the council.
Mr Hamer's daughter Ruth Topping said: "I hope the authorities will learn lessons as I do not want my father to have died in vain.
"I do not want any other family to suffer like we have suffered or like my father suffered - he had an horrific death."
The jury found that hitting a pothole had probably contributed to  Mr Hamer, from Ramsbottom, coming off his bike on a road which had several defects.
Its narrative verdict said Bury Council had "followed repair guidelines" but found there had been inconsistencies in the way it dealt with some repairs.
The authority said it had learned lessons and was improving its training. It added that Bury New Road would be fully resurfaced by next March.
The coroner is writing to both the Department of Transport and Bury Council highlighting a number of concerns raised during the inquest.

Leader Grenville Ham said community-run renewable energy schemes and "truly efficient" housing could provide jobs for thousands of people.
"Across Wales, Greens have the expertise and the appetite to develop sustainable local economies that provide jobs for all," he said.
The party currently has one Welsh councillor and 50 confirmed candidates.
"As a party, we are focusing on reducing fuel bills through local selling of locally-generated renewable energy," Mr Ham said.
"My vision is to cut out the exploitative middle man in energy production and delivery, through Green-led local action."
Mr Ham added that Green councillors would not be told by party bosses how to vote on issues.
"We believe that our candidates know their local community best," he said.
Ticket offices will start closing on the London Underground later in a move that has prompted past strikes.
[NEXT_CONCEPT]
An 83-year-old cyclist who was flung 20m (65ft) from his bike and later died "probably" hit a pothole, an inquest jury found.
[NEXT_CONCEPT]
The Wales Green Party has launched its campaign for the local elections, pledging to "rebuild" communities.