Under the terms of the agreement brokered by the US, Ghani would be the new president of the country while Dr Abdullah would occupy the post of chief executive officer.
The White House said Obama spoke with Ghani and Dr Abdullah to congratulate them on concluding their agreement for a government of national-unity and safeguarding the first democratic and peaceful transfer of leadership in Afghanistan's history.
Obama thanked them for their leadership and willingness to partner to advance Afghanistan's national interests, the White House said.
In a separate statement, Congressman Ed Royce, Chairman of the House Foreign Affairs Committee, said Afghanistan will now transition from one elected leader to another.
"The Afghan people can be proud of the role they played. The election, especially the tabulation, has been rough but there is cause for hope if things change.
"After nearly 13 years under the failed policies of the Karzai administration, Afghanistan desperately needs a fresh start with a new leader and innovative ideas," he said.
Afghanistan otherwise will be a failed state, with disastrous consequences for Afghans, and greater dangers to US national security, he said.
Royce also added that "President-elect Ghani must confront many challenges, including rampant corruption, revenue shortfalls, and a very challenging security situation."
"I look forward to working with him and Abdullah Abdullah to ensure that Afghanistan remains a key security partner of the United States," he said.
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