His pledge came only days after US President Barack Obama said the 32,000 American forces in Afghanistan will be scaled back to 9,800 by early 2015 and complete a full withdrawal by the end of 2016.
"I'm committed to signing a bilateral security agreement within the first week of taking over," Ghani said, addressing an audience in Washington via Skype from the western Afghan city of Herat.
"The reason is that our national security forces need assurances regarding our global partnerships and the resources both human and material that would come through the bilateral security agreement," Ghani told the Atlantic Council think-tank.
He is facing off against former foreign minister Abdullah Abdullah, seen as the front-runner in the June 14 second round.
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But Ghani faces an uphill task after finishing second with 31.6 per cent -- behind Abdullah with 45 percent -- in the eight-man first round on April 5.
Outgoing President Hamid Karzai has refused to sign the long-delayed Bilateral Security Agreement (BSA) laying out the terms of the US military presence once most combat troops leave at the end of this year.
Obama's new framework "telescopes a process that previously we might thought would take 10 years," Ghani said.
The plans also refuted claims by militant Taliban and Al-Qaeda insurgents that the US is "seeking permanent bases in Afghanistan" which means in the next two years the peace process "is going to have to take center stage," he said.
Ghani vowed to seek better regional ties with neighbors such as Pakistan, which he envisioned as a decade-long process, saying the two countries "can engage in the type of dialogue that France and Germany engaged in after World War II" and foreseeing that they could become "pillars of regional stability.