"The first flight will be to Dubai on Sunday evening and will be followed by regular flights immediately afterwards" to Bahrain, Damascus, Amman and Beirut, al-Barges said on Saturday.
The airline's operation includes daily flights from Kuwait City to Dubai, Beirut, Damascus and Manama, and three flights a week to Amman. It also plans to operate to Egypt, India and southeast Asia later.
Jazeera initially planned to start operations in February using two leased planes; but the airline later decided to delay its launch until it received its own aircraft.
The company on Monday took delivery of one of four Airbus A320s it has ordered. The second plane is due to arrive next week while the remaining two are scheduled for delivery in June.
Jazeera was established in May 2004 as a shareholding company with a capital of $34 million, 30% of which is owned by a group of core founders while the rest was offered to the public on 26 May.
The airline was founded by Boodai Group, a leading Kuwaiti business group which has key investments in the media, transport and aviation sectors.
The first Airbus 320 of Jazeera
Airways is seen on the tarmac
The Kuwaiti government, in November 2003, had opened the domestic aviation sector to competition by allowing the private sector to establish low-fare passenger and cargo airlines to compete with the state-owned, loss-making Kuwait Airways Corporation (KAC).
A second private aviation company for cargo is also being established.
The decision came after the Gulf Arab emirates of Sharjah and Abu Dhabi, in 2003, began operating their own airlines, with Sharjah's Air Arabia billed as the first no-frills carrier in the Middle East.
Jazeera is offering fares for as little as 40% of the normal rate in the emirate. Travellers in Kuwait can fly to Manama one way for $34.
KAC reacted to Jazeera's launch by offering a 50% discount to the new airline's five destinations for one month starting on 5 November.
The move was seen by local observers as a price war against the new company, but Barges said the market is open for various operators.
KAC has incurred a loss almost every year in the past decade, and its total accumulated deficits have reached hundreds of millions of dollars.