General Guei has also announced measures including the dissolution of parliament, government, the constitutional council and the supreme court.
French diplomats negotiated the ousted president's safe passage out of Ivory Coast, reports say.
The ousted president sought refuge at the French embassy earlier in the week, when General Robert Guei's supporters took to the streets.
The French news agency, AFP, reported that President Bedie was at the airport in Abidjan and waiting for a plane to take him out of the country.
General Guei has appeared on national television several times, to announce that he was in control and to promise respect for democratic rule.
The general also said: "Power is in my hands. I will take care of everybody. You should not be worried."
President Bedie had earlier called for fellow Ivorians to resist the military coup.
He spoke to French International Radio from the capital Abidjan.
"I am at my post; I am in the official residence in Abidjan. The nitwit who has proclaimed himself president of the republic has, at this very moment, dissolved the National Assembly, the Constitutional Council and other institutions of the republic. This is unacceptable."
He went on: "I am therefore maintaining those institutions, calling on them to refuse to obey. I am urging them to organise resistance and I am calling on their supporters to back the civil resistance movement against the seizure of power by force."
Gunfire and looting
Scattered gunfire has been reported around Abidjan. Soldiers and civilians looted certain parts of the city.
Mobs of youths are reported to have taken advantage of the vacuum in law and order to hijack cars and mug people trying to get home before the 6 PM curfew.
General Guei has also announced measures including the dissolution of parliament, government, the constitutional council and the supreme court.
The rebels took control of Abidjan Airport on Friday.
The rebels also opened prison gates to release political prisoners, allowing other inmates to escape as well.
Mutineers have taken control of key bridges, and set up checkpoints.
A Military Committee of Public Salvation called on looting to stop and said an overnight curfew would be imposed.
It said the takeover of power had been carried out to restore soldiers' dignity.
The soldiers' biggest complaint was understood to relate to unpaid bonuses from a UN peacekeeping operation in the Central African Republic in 1996 and 1997.
Defence Minister Bandama N'Gatta told journalists that four mutineers had met ministers and laid down nine demands.
Mr N'Gatta said the UN had not paid all of what it owed Ivory Coast after the first mission, "and we have not received anything under the second, which started 10 months ago and winds up in February".
Lack of decent housing and even shoes are among the other grievances that have been reported.