The decision to play two matches instead of the usual one was taken after discussions between the KNVB, both clubs and local authorities in Amsterdam and Rotterdam.
Ajax will host Feyenoord on April 25 with the return in Rotterdam on May 6. Both matches will be played without fans from the visiting club.
"The enormous costs of security and the flaring up of hostilities between both fan groups in the last few weeks are the reasons for this decision which is supported by all involved parties," KNVB-director Henk Kesler told a news conference.
"Also the Minister of Home Affairs showed great concern about the costs of approximately one million euros for security and the possible social unrest."
Two years ago the mayors of both cities decided that away fans would be banned from matches between the teams for five years after a series of violent incidents.
The traditional rivalry between Feyenoord and Ajax reached a lowpoint in 1997 when hundreds of fans clashed in a meadow near Beverwijk with several people wounded and one killed.
Since 1989 the Dutch Cup final has been held at Feyenoord's home stadium in Rotterdam.
For the scheduled one-match final the KNVB and the mayor of Rotterdam first agreed to allow 10,000 fans from both teams into the stadium with a capacity of 48,000.
But this week fans from both clubs said they had obtained tickets for the neutral zones in the stadium.
