The Rail Maritime and Transport (RMT) union had called a 48-hour walkout for February 12 and 13 in a long-running dispute over pay and disciplinary procedures.
But the strikes will now be held from noon on Monday February 11 to noon the following day and again from noon on Wednesday February 13 for 24 hours.
The change will mean that SWT services will be disrupted over four days, causing fresh travel misery for hundreds of thousands of rail users across southern England.
The union's acting general secretary, Vernon Hince, accused the company of prolonging the dispute.
"Instead of using every endeavour to settle the dispute South West Trains are wasting time and money training managers and other willing stooges to undertake RMT members' duties.
"The dispute will not go away just because SWT don't want to negotiate. Passengers should rightly be furious that rather than trying to resolve the dispute the company is actively seeking to prolong it."
Andrew Haines, managing director of SWT, said: "This shows new heights of cynical disregard from the RMT to cause maximum disruption to our passengers.
"We will do our very best to minimise any disruption and will run as many services as possible."
SWT ran hundreds of trains during a 48-hour strike last week when managers stood in for striking workers.
The company had said it would run 800 services next week - compared to the normal daily total of 1,700 - before today's announcement of new strike dates.
The 350,000 passengers who use SWT services every day have already been hit by three 48-hour strikes since the start of the new year because of the increasingly bitter row.
The company has imposed a 7.6% pay rise over 18 months after reaching deadlock in talks with the RMT over wage rises.
SWT also rejects union allegations that it has been heavy-handed in demoting RMT activist Greg Tucker.
