Gen Indjai led a mutiny in April, ousting the head of the army, who is still in custody, and briefly detaining the prime minister.
The US has questioned the government's control of the armed forces and has now broken off military aid.
Last week, it asked for suspected drug lords in the military to be removed.
In recent years the tiny West African nation has become a major transit hub for cocaine smuggled from Latin America to Europe and has suffered much political unrest as a result.
It has more than 80 largely uninhabited islands off its coast which are handy smuggling points for traffickers.
President Malam Bacai Sanha defended his decision to appoint Gen Indjai, who was army vice chief of staff before the mutiny.
"We took a sovereign decision to name Gen Indjai as the head of the army, because Guinea-Bissau is a sovereign country. I am speaking as the democratically elected president," AFP news agency quotes Mr Sanha as saying.
In April, days after the mutiny, Guinea-Bissau's air force head Ibraima Papa Camara and former navy chief Jose Americo Bubo Na Tchuto were named by the US as "drug kingpins", and had their US-based assets frozen.
Correspondents say Mr Na Tchuto, who is still hugely influential behind the scenes, was at the inauguration ceremony.
He was freed by some soldiers during the April mutiny from a UN building in the capital, Bissau, where he had taken refuge since December last year.
He had returned to the country after spending a year in exile in The Gambia following a coup attempt he was accused of leading in 2008.
Last month, the European Union suspended its mission to help with reforms of Guinea-Bissau's military until the government clarified what had happened in the mutiny.
A heads of state meeting of the regional West African grouping Ecowas, which starts on Thursday in Cape Verde, is expected to discuss the crisis in Guinea-Bissau.
Cape Verde's foreign minister told the BBC's Portuguese Service that Brazil's President Luiz Inacio Lula da Silva would attend an Ecowas gathering on Saturday and fly to Guinea-Bissau the following day.Source: BBC (30/06/2010)