Also on hand were France's defence minister and the most senior US delegation to visit the country.
US looking forward
"The transition to a democratically elected government opens the way ... towards a significant expanded co-operation between us," John Negroponte, US deputy secretary of state, said after congratulating the Mauritanian president.
"Whatever government he forms, we look forward to collaborating with it closely and to deepening our relationship with this country."
He said Washington would expand co-operation on health, education and security.
Abdallahi is a 69-year-old former political prisoner and ex-government minister who won 52.85 per cent of the votes in a second round run-off against Ahmed Ould Daddah, a veteran opposition leader.
He will serve under a new constitution which limits the number of presidential terms to just two five-year terms and sets a maximum age of 75 years for a president.
Previous presidents in this vast and largely desert country have seized power in coups or autocratically ran the country after being re-elected in elections marred by fraud.
A 17-member military junta that ousted former authoritarian ruler Maaouiya Ould Taya in 2005, surprisingly embarked on a series of sweeping democratic reforms capped by the presidential vote declared free and fair by international observers.
The junta has declared the "commitment of the armed forces to loyally serve the new institutions".
After Thursday's pomp and fanfare, Abdallahi faces huge challenges of uniting the racially diverse country, still battling with its recent legacy of slavery.
Half of the country's 3.1 million inhabitants live under the poverty line, despite the opening of offshore oil fields a year ago.
He has to ensure the equal distribution of the oil wealth which started flowing into one of Africa's most impoverished countries.