FORT CAMPBELL, Ky. — A grateful President Obama yesterday shook the hand of the Navy SEAL who shot and killed terror nemesis Osama bin Laden.

At Fort Campbell, one of the nation’s largest military bases, Obama met privately yesterday with members of the assault force that carried out the mission to get bin Laden, thanking each one individually for their “heroic and selfless service” to the country.

Obama then awarded the SEAL teams the “Presidential Unit Citation” — the highest honor a unit can get, in recognition of their “extraordinary service and achievement.”

He called the commandos that completed the steely nighttime mission “the finest small fighting force in the history of the world.”

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Obama and Vice President Biden also met with 160th Special Operations Aviation Regiment — the so-called “Night Stalkers” — who transported the force into Pakistan by stealth helicopter under cover of darkness, and Green Berets from the 5th Special Forces Group.

The SEALs gave Obama a briefing on the mission complete with a scale model of bin Laden’s hideout in Pakistan and maps.

“In each meeting, the president was able to speak and offer his personal admiration and gratitude for our service-members, and to personally greet them,” said a White House official.

“Job well done,” Obama said after the private meeting the special forces when he got a chance to address about 2,000 troops at a huge hangar at Fort Campbell, home to the 101st Airborne Division’s famous “Screaming Eagles.”

“They trained for years,” Obama said, praising the special-forces unit when he spoke to the Airborne troops who had just returned from Afghanistan. “When I gave the order, they were ready.”

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Obama called the daring mission into bin Laden’s hideout in Abbottabad, Pakistan, “one of the greatest intelligence and military operations in our nation’s history.”

The president even met Cairo, a dog that took part in the mission and helped alert the special forces teams to hidden threats, an official said.

The dog is the only member of the raid team to be identified by name so far.

The hangar where he spoke was decorated with a huge American flag. Another huge banner said simply: “Job Well Done.”

Obama got an ear-splitting welcome from the troops, a few of whom high-fived immediately after his speech.

“It brought us up a whole lot . . . especially for the guys who just came over here” from Afghanistan, said Eddie Brown, a transportation specialist who himself just returned from a deployment. “Us catching Osama bin Laden is kind of helping us to know we’re actually doing something over there.”

Army troops making steep sacrifices of their own had high praise for the special operators who successfully completed their daring mission.

“It’s awesome,” said Derek Zotto, an executive officer just back from Afghanistan. “It’s something that you see in Hollywood movies, but they pulled it off.”

Obama said the United States and allies have seized momentum in Afghanistan, and promised, “We are ultimately going to defeat al Qaeda.”

geoff.earle@nypost.com

