"It is an opportunity for great pride and happiness that members of the Loya Jirga came to a total agreement on the constitution," chairman Sebghat Allah Mujaddidi told the 502 delegates on Sunday.
The historic document, agreed after three weeks of heated debate, will pave the way for Afghanistan's first democratic elections in June.
Under the provisions of the landmark document, the presidential system favoured by President Hamid Karzai has been approved, but with two vice-presidents instead of the original one.
But delegates failed to reach a consensus on a national language, an issue which had delayed a final agreement on a constitution.
The draft constitution is due to be ratified by a vote shortly.
Minorities such as Uzbeks feared they would be sidelined by the new constitution, whereas Pashto-speaking Pashtuns (who represent about 40% of Afghans) argued their language was spoken by a majority and should be the sole national tongue.
Delegates secured changes to
the original US-backed draft
There has been a long standing rivalry between the Pashtuns, who have traditionally dominated Afghan political life, and smaller groups such as the Dari-speaking Tajiks and Uzbeks.
Delegates finally agreed Pashtu and Dari would serve as the country's official languages, but other ethnic minority languages would also be considered official languages in the areas where they are spoken.
The Loya Jirga has been meeting under tight security in the Afghan capital Kabul since 14 December.
The US, which overthrew the former Taliban government in late 2001, is encouraging the formation of new government drawn from Afghanistan's diverse communities that can withstand a growing threat from regrouping Taliban forces.