Israel Radio reported that the ultra-Orthodox Shas party, a key coalition partner of Olmert, threatened to quit the government unless the construction was approved.
Eran Sidis, a spokesman for Zeev Boim, the Israeli housing minister, said the decision was taken after consultations with Olmert.
Olmert has barred ministries from ordering new Israeli construction in the West Bank without his approval because of its political rammifications.
The latest approval effectively reverses a freeze on settlement expansions in the West Bank made after US-brokered talks in Annapolis.
A previous understanding between Olmert and the US differentiates between settlement expansion in east Jerusalem and the West Bank. Although the distinction is not consistent with international law, which holds settlements in both areas as illegal, the US has indicated that it primarily opposes expansion in the West Bank.
|The announcement came days after seminary|
students were killed in Jerusalem [AFP]
Sidis said a plan to build 750 housing units in Givat Ze'ev was approved in 1999 but suspended two years later after the Palestinian uprising led to a shortage of construction workers.
Under the current plan 200 units will be built initially and another 550 in the future.
Zeev Boim released a statement saying, "The renewal of the [project] is important news."
"The addition of hundreds of housing units is part of a policy aimed at meeting demand and keeping prices level, while addressing the demographic needs of Jerusalem," the statement said.
Israel has said in any future peace agreement with the Palestinians it intends to annex Givat Ze'ev, which is home to 10,000 Israelis, into a "Greater Jerusalem".
It also wants to retain several other major settlement enclaves in the West Bank, which Palestinians hope to make part of a future state.
Last week, Mahmoud Abbas, the Palestinian president, suspended talks after a five day Israeli military offensive in the Gaza Strip killed more than 120 Palestinians.
Abbas agreed to resume talks, which are expected to get under way later this week, following a visit by Condoleeza Rice, the US secretary of state.