The mission, designed to supervise the work of Palestinian security and customs officers, will come on top of a European Union mission to train police scheduled to start in the Palestinian Territories on January 1.
"We are going to take responsibility as a third party in Rafah," EU foreign policy chief Javier Solana told a news conference after a meeting of EU foreign ministers.
"Now we have the most important security presence in the Middle East ever taken by the European Union ... We are entering also the security aspect," he added.
Rafah is on the border between the Gaza Strip and Egypt.
Israel, which quit the Gaza Strip in September after 38 years of occupation but controls the territory's borders, has been under US pressure to reopen Rafah to Palestinian trade and travel, as a step to encourage peacemaking.
Some 1.4 million Palestinians live in the strip Israel captured in the 1967 Middle East war.
Israel had accepted an Egyptian proposal to let Palestinians travel freely across Rafah with foreign oversight but then delayed a cabinet vote on Sunday when disagreement surfaced as to what role the monitors would play.
The EU will also launch a police mission to boost the Palestinian police from the beginning of next year.