"We have held talks with the centre-right parties and also with the Left. Now we are agreed that we should proceed so that the Financial Supervisory Authority (FI) can impose amortization requirements," Finance Minister Per Bolund said on Saturday.
The agreement also contains a number of exemptions from the amortization requirement.
"To reduce the possible impact on residential construction, exceptions should apply, for example, when purchasing newly built homes. Exemptions should also be granted in certain special circumstances such as unemployment, illness, divorce or bereavement," the finance ministry explained in a statement.
The new law is now due to come into force on May 1st 2016.
Earlier plans to introduce the requirement were scrapped by the financial watchdog in April following a ruling by an administrative court in Jönköping in southern Sweden which indicated that the proposed changes were not supported by Swedish law.
The plan is designed to help stabilize the country's economy which is characterized by high levels of household debt as experts warn of an inflationary housing bubble.
Unlike in other countries, many Swedes currently only pay back the interest on their mortgages.
Under the original plans to change this
, customers would have been asked to pay two percent of the value of their mortgage every year until they had repaid 30 percent of the loan. They would then have been required to pay at least one percent a year until they hit the 50-percent mark.
Since the court's ruling the matter has been left for the government to deal with.
A few weeks ago the Riksbank, Financial Supervisory Authority and the Swedish National Debt Office issued warnings in a coordinated move to try to push the political parties to hammer out an agreement.