The operator's owners lost a legal bid to halt the walkout, which will mean many commuters will have to work from home, take time off, or attempt to drive because of the huge disruption.
Members of the drivers' union will strike on Tuesday, Wednesday and Friday in a dispute over driver-only trains.
Charles Horton, chief executive of Southern's parent company Govia Thameslink Railway (GTR), confirmed there will be no services on strike days and "severe disruption" during an ongoing overtime ban.
The shutdown of Southern's services will be the worst disruption since the railways were hit by a lengthy strike by signal workers in the mid 1990s.
RMT drivers on Southern will also be on strike, while the guards will launch a fresh 48-hour walkout from next Monday, and a three-day stoppage from New Year's Eve.
GTR lost a legal bid in the High Court last week to stop the drivers' strikes, before also losing its appeal on Monday.
Three judges in the Court of Appeal backed High Court judge Sir Michael Burton's refusal to grant an injunction blocking what GTR called "unprecedented" strike action and argued would unlawfully restrict freedom of movement provisions under EU law.
Lord Justice Elias, Lord Justice Lewison and Lord Justice Lloyd Jones also said they were not prepared to grant an injunction.
Around 300,000 passengers travel on 2,242 Southern services every weekday, including busy commuter routes from Sussex to London Victoria.
They have suffered months of disruption because of the Aslef dispute and a separate row with the Rail, Maritime and Transport (RMT) union over changes to the role of guards, as well as staff shortages, staff sickness and other problems such as signal failures.
Aslef is also planning a week-long strike from January 9.
Mr Horton said he was "disappointed" at the Appeal Court's decision and called for fresh talks at the conciliation service Acas.
He said: "We strongly advise people not to travel. In addition, there will be severe disruption every day during the ongoing industrial action because of the union's overtime ban.
"We will now be asking Acas to convene urgent and immediate talks between GTR and Aslef. Our aim is to find a resolution to their dispute so we can bring an end to the misery being suffered by the travelling public."
Aslef general secretary Mick Whelan said drivers had been forced to strike because of the company's "intransigence".
He said: "We have tried everything possible this year to reach a sensible and workable compromise with Southern in the interests of passengers and management as well as of staff.
"We have always been prepared to sit down and talk, because we have always believed it is, or should be, possible to do a deal - as we did with ScotRail - but the company, encouraged by the Department for Transport, has not been prepared to negotiate with us."
Aslef denied company claims that it had refused to attend peace talks over the weekend.
Mr Whelan said Southern Railway had contacted him to suggest going to Acas late on Sunday, but Aslef said it would do so only if the company called off the court action.
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