Stoltenberg said Norway would offer annual aid of 750 million kroner ($137 million) to the war-torn country which is one of the poorest and most corrupt in the world.
He said that the aid agreement -- which formalizes previously made pledges – would depend on Afghan authorities' commitment to "good governance, the rule of law, human rights, transparency and democracy."
"We have zero tolerance for corruption," he stressed, noting that Oslo had suspended development aid in the past when funds had been misappropriated.
According to graft watchdog Transparency International, Afghanistan, which is the second-biggest recipient of Norwegian aid, is ranked as one of the most corruption-riddled countries in the world alongside North Korea and Somalia.
During his visit on Tuesday, Karzai said that he plans to step down next year when his mandate expires.
"The question of me staying as the president beyond 2014 is out of the question," Karzai said when reporters asked about recent speculation that he was keen to stay on.
"Neither am I seeking a third term, nor does the constitution allow it. There will be an election and a new president will come," he said.
Karzai has previously said he would not stay in power beyond 2014, including at a meeting with US President Barack Obama last month, amid some concern that he could try to cling to power.
Karzai was elected in 2004, and re-elected in 2009 in a vote marred by accusations of fraud.
Afghanistan's next presidential election is scheduled for April 2014, just a few months before the end of NATO's mission.