The US fears any incursion could destabilise the region
The vote was taken in defiance of pressure from the US and Iraq, which have called on Turkey for restraint.
Turkish Prime Minister Recep Tayyip Erdogan has said the motion does not mean a military operation is imminent.
But he said Turkey needed to be able to respond to a recent rise in bomb attacks blamed on PKK rebels from Iraq.
Turkish MPs backed him overwhelmingly, by 507 votes to 19.
As the vote was being counted, US President George W Bush strongly urged Turkey, a key ally, not to carry out the threatened action.
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He said Washington was "making it clear to Turkey it is not in their interest to send more troops in... there is a better way to deal with the issue".
The recent deaths of 13 Turkish soldiers in an ambush blamed on the PKK has put the government under renewed pressure to respond with force.
What Turkey wants now is a convincing response from allies and neighbours, says the BBC's Sarah Rainsford in Ankara.
Turkey has been calling for help in tackling the PKK for months. Now it hopes the rest of the world will realise it is serious, our correspondent says.
'Illegal'
But the US and Iraq fear any incursion could destabilise the only relatively calm region of Iraq.
Iraqi Prime Minister Nouri Maliki phoned the Turkish prime minister before the vote, saying he was "absolutely determined" to remove the PKK from Iraq and pleading for more time, according to Turkey's Anatolia news agency.
Iraqi President Jalal Talabani, an ethnic Kurd, urged Turkey not to make an incursion, but also called on the PKK "to end the so-called military activity".
The autonomous Kurdish regional government in northern Iraq warned Turkish MPs that any intervention would be "illegal". It has denied providing the PKK with any help.
HAVE YOUR SAY They have no right to enter Iraq and I hope that they will be resisted strongly with all available resources should they try
Mike, Surrey
Send us your comments Iraqi Kurds give their views Explosive potential of raid
The rebels themselves said they would meet force with force.
The chief of the PKK's executive council, Murat Karayilan, told the Kurdish Hawlati newspaper: "Thousands of PKK guerrillas are on standby to fight Turkish army forces."
However Syrian President Bashar Assad, visiting Turkey, said he supported the country's right to take the action "against terrorism and terrorist activities".
Armenian question
President Bush, speaking during a press conference, criticised the US Congress for jeopardising US relations with Turkey with a planned vote to recognise the mass killing of Armenians in Ottoman times as genocide.
"One thing Congress should not be doing is sorting out the historical record of the Ottoman Empire," he said.
Although a congressional committee has supported the motion, its chances of passing a full vote appear to be waning.
Key Democrats in the US House of Representatives have joined Republicans to warn that US strategic interests could be damaged by the largely symbolic resolution.
Turkey.
On Wednesday, Turkey's Grand National Assembly voted 507-19 to authorize sending troops into northern Iraq to pursue Kurdish rebels.  Although the authorization is valid for one year, Turkish officials made clear that it would not necessarily result in military action.  Both the United States and Iraq have recently warned Turkey against such an incursion.  

Turkish Prime Minister Recep Tayyip Erdoğan said that although the motion does not indicate that a military operation is imminent, it is necessary for Turkey to be able to respond to bomb attacks which have been blamed on Kurdistan Workers Party (PKK) rebels in Iraq.  Turkey has been asking for help in dealing with the PKK for months, and the Turkish public has grown frustrated with America's perceived lack of action on the issue. 
Map showing Kurd-inhabited region overlapping national borders.
Both the United States and Iraq have recently warned Turkey against an incursion into Iraq.  "The Iraqi government calls on the Turkish government to pursue a diplomatic solution and not a military solution to solve the problem of terrorist attacks which our dear neighbor Turkey has witnessed from the PKK," Iraq government spokesperson Ali al-Dabbagh said earlier this week.  White House National Security Council spokesman Gordon Johndroe called on Turkey "to continue their discussions with us and the Iraqis and to show restraint from any potentially destabilizing actions."  

Responding to the motion, U.S. President George W. Bush urged Turkey not to carry out an attack, saying "we are making it clear to Turkey it is not in their interest to send more troops in... there is a better way to deal with the issue."

Syrian President Bashar al-Assad defended Turkey's decision and criticized the U.S. position, saying "It is important to note that the powers that have invaded Iraq are those primarily responsible for the terror activities and attacks because they control the country."  "We certainly support and back the decisions by the Turkish government in combat against terror and terror activities," he said.

Murat Karayilan, the leader of the armed wing of the PKK, warned Turkey of the consequences of an attack in an interview with The Times.  "If the Turkish Army attacks Iraqi Kurdistan we will struggle and resist against this until the end," he said.  Karayilan nevertheless said he hoped that the crisis could be resolved peacefully but continues attacks on Turkish soldiers, killing 12 in an ambush yesterday.

U.S.-Turkish relations have been strained recently after a U.S. House of Representatives resolution passed committee, labeling the World War I era killings of up to 1.5 million Armenians by the Ottoman Empire as "genocide". Turkey strongly disputes these claims. Majority Leader Nancy Pelosi says the US House of Representatives will vote on the resolution "soon."

President Bush criticized the resolution at a press conference on Wednesday, saying "One thing Congress should not be doing is sorting out the historical record of the Ottoman Empire."