The train firm said it would refund the difference in cost between mainline and high speed fares - to compensate for the loss of direct high speed trains.
Southeastern will also give season ticket-holders from five stations a backdated 20% refund on mainline fares.
Dover MP Charlie Elphicke, said the line still needed repairing quickly.
He said it had been a difficult time for rail users and it was right passengers should be compensated after the problems were caused when cracks appeared in the sea wall.
Mr Elphicke said an emergency peak-time high-speed rail service between Dover and St Pancras to help commuters had made a difference.
"We now need Network Rail to confirm how long it will take to repair the sea wall," he said.
Steve Kilby, from Network Rail, said the team was working hard to get a final design in place for repairs.
But, he said: "This week has been very stormy on the beach and our guys have been working through tough conditions."
He said 15,000 tonnes of rock had been placed on the shingle to protect the railway from heavy seas and eventually more than 70,000 tonnes would be in place.
The stations where passengers will be compensated are Sandwich, Deal, Walmer, Martin Mill and Dover Priory.
Compensation claim forms are available for people at the station.

The remains of Saima Ahmed, 36, were recovered from the grounds of Gogar Mount House, on the edge of Gogarburn Golf Club.
Her family have criticised the police response after they reported Ms Ahmed missing from her home in the Wembley area of London in August 2015.
She had no known links to Edinburgh.
Ms Ahmed's family were also unaware of any friends or contacts she might have had in the area, or any plans to travel to Scotland.
Five Metropolitan Police officers are now facing a misconduct investigation over the case.
Police Scotland have said that, to date, no suspicious circumstances surrounding Saima's death have been discovered.
Det Ch Insp Martin MacLean said: "I am determined to provide Saima's family with the answers they crave and whilst, at this time, I have no evidence of any criminality, I still do not know why Saima travelled to Edinburgh, where she was intending to visit or whom she planned to meet with.
"I thank those who have helped us thus far, but I believe someone out there will have seen Saima during her time in the city or knows why she visited the capital and I would ask that person, or persons, to contact police immediately.
"In addition, anyone with any further information at all relevant to this ongoing investigation is also asked to get in touch."

The yellow warning will remain in force until 11:00 on Sunday.
Forecasters said showers accompanied by widespread sub-zero temperatures would see ice form on many untreated roads.
Some snow is expected even at low levels in northern Scotland and other areas could see 2-3cm fall on higher ground.
A Met office forecaster said: "Over northern Scotland showers will fall as snow to low levels.
"Elsewhere within the warning area these showers will be turning increasingly wintry, with the main snow level down to between 100 and 200m by the end of the night.
"Locally 2 or 3cm of snow is possible above 200m."

A series of abusive Twitter remarks were posted on an account on Tuesday, directed to Flower, who was sent off in Saturday's Super League Grand Final.
Flower received a six-month ban for hitting St Helens stand-off Lance Hohaia.
One comment on the single account said Flower's "last days are approaching".
Other Twitter messages said that Flower "deserves to be shot", adding that he  is a "dead man".
Greater Manchester Police (GMP) tweeted: "We've been made aware of abusive social media activity about the Rugby League Grand Final. Please be reassured that we are looking into this."
More than 70,000 fans at Old Trafford and millions of television viewers saw the player hit Hohaia, who lay motionless on the ground just two minutes into the match.
St Helens chairman Eamonn McManus said after the ban: "We must assist [Flower] in any way that we can and accept him back into the sport. There is a person behind the player, and I am reliably informed by all that it is a good one."
Mr McManus also said of the punching incident: "These matters have to be dealt with by the appropriate body within the game and it has so been."
A GMP spokesman said any decision to take action against Flower would depend on conversations it had with St Helens.
Passengers affected by the collapse of a railway line during storms in Dover are to be compensated, rail operator Southeastern has said.
[NEXT_CONCEPT]
Police have made a fresh appeal for information a year after a woman's body was found on the outskirts of Edinburgh.
[NEXT_CONCEPT]
A  weather warning has been issued for most parts of Scotland, with drivers urged to be aware of a risk of ice and snow.
[NEXT_CONCEPT]
Death threats made against Wigan rugby league player Ben Flower, who punched an opponent as he lay on the ground, are being investigated by police.