The Department for Transport said more than 84,000 passengers will be compensated against the huge amount of delays, cancellations and disruption on the network this year.
The problem has partly been due to strikes over changes to the role of conductors and high levels of staff sickness.
Rail minister Paul Maynard said: “Getting Southern rail services back on track is a priority for the Government and I know that what passengers want most is a reliable service.
“But when things do go wrong it is right that we compensate people who have not had the service that they deserve. This is a gesture in recognition of the problems people have faced.
“We’re working hard to get Network Rail and Southern to improve this network and get this railway working the way people expect.”
Season ticket holders will be able to claim a refund for the equivalent of a month’s travel.
Passengers with an annual ticket will be able to claim the “one off” payout against their 2016 ticket, which can be paid directly into their bank account. Customers claiming against quarterly, monthly or weekly tickets must have bought travel for at least 12 weeks between April 24 and December 31 to be eligible.
The Government said GTR, the parent company of Southern, has the details of most season ticket holders and it will be inviting them to log on to a website to claim compensation.
The company will also be able to consider proof of purchase from people claiming a payout who have not previously registered.
It comes as the rail industry announced train fares will go up by an average of 2.3 per cent next year.
Rail, Maritime and Transport union general secretary Mick Cash said the fare hike, beginning on January 2, is a “another kick in the teeth for British passengers”.
“Once again the rip-off private train companies are laughing all the way to the bank as they whack up fares and axe staff in all-out dash to maximise their profits,” he said.
“This culture of private greed on Britain’s railways has to stop and RMT will step up the fight for a publicly-owned railway where services and safety are the priority, not corporate profits.”