Thousands of Zelaya's supporters rallied under a hot sun and police supervision at the airport to bid their former leader farewell.
Zelaya's four-year term was to have ended on Wednesday, the same day Lobo was sworn in during a ceremony attended by few international dignitaries.
Lobo's first act upon taking office was to sign a decree giving amnesty to the soldiers, politicians and judges behind the June 28 coup against Zelaya.
He said the measure - first proposed months ago in failed mediation talks in Costa Rica backed by Washington - was needed as part of a process of national healing.
Lobo, 62, replaces a conservative interim government headed by Roberto Micheletti, which was not recognised by other countries after the coup.
Arturo Valenzuela, the US assistant secretary of state for western hemisphere affairs, was among the guests at the presidential swearing-in ceremony - a sign of Washington's support for Lobo.
Others included presidents Fernandez, Ricardo Martinelli of Panama, and Ma Ying-jeou of Taiwan, as well as Francisco Santos, the Colombian vice-president.
|Zelaya was holed up in the Brazilian embassy for more than four months [AFP]
France said it was "ready to support the new Honduran authorities" as Lobo embarked on a period of national reconciliation, a foreign ministry spokesman said in Paris.
But leftist governments across the region, including powerhouse Brazil, broadly reject his route to power, seen as stemming from and potentially legitimising the coup in a region with a painful history of political upheaval and military rule.
"For Brazil, the situation has not changed. For now, Brazil does not recognise Lobo's government," an official in Brazil's foreign ministry told the AFP news agency.
Zelaya has been holed up in the Brazilian embassy since sneaking back into Honduras in September, following his forced deportation by soldiers acting under orders from the supreme court.
Lobo, who was elected in controversial November polls called by Micheletti, faces several challenges to repair the damage from Zelaya's overthrow.
The most immediate ones are filling state coffers starved of trade revenues and foreign credits, and engineering Honduras' return into the family of Latin American nations outraged by the June coup.
Honduran politicians and senior judges said they conspired to topple Zelaya because he was threatening the constitution by trying to stay in power beyond his single permitted four-year term.
A Honduran judge on Tuesday dismissed all charges against six military commanders who helped organise the coup and congress was expected on Wednesday to approve an amnesty for Micheletti and all involved in Zelaya's removal.