The former finance minister was inaugurated, marking Afghanistan's first democratic transfer of power since the fall of the Taliban in 2001, Al Jazeera reported.
Ghani succeeds Hamid Karzai after a three-month standoff over disputed election results.
Both Ghani and rival Abdullah Abdullah claimed to have won the June 14 election, plunging Afghanistan into a crisis.
But, under pressure from the US and UN, the two candidates eventually agreed to form a national unity government, and Ghani was declared president after an audit of nearly eight million ballot papers.
Abdullah will also be sworn in as chief executive, a new role similar to a prime minister, in a government structure far different to Karzai's all-powerful presidency.
"We made a lot of effort to bring about a long-lasting peace, but unfortunately our hopes did not fully materialise, but I should say that peace will surely come," Karzai said during farewell speech late Sunday.