Opposition leader Silvio Berlusconi, who is currently ahead in opinion polls, has in the past criticized the sale to Alitalia's long-time partner and European neighbor, saying he favours an Italian solution.
The takeover would end the 60-year independence of a global Italian brand but would also avoid the flagship airline going broke as its cash reserves quickly dry up while the European Union has banned any more state aid.
The airlines said Air France-KLM had offered one share for every 160 shares of Alitalia as part of its binding offer, valuing Alitalia's stock at 0.10 euros a share -- an 81 percent discount to the record low price seen at Friday's close.
That price is well short of the 0.35 euros per share which Air France-KLM was said to have initially bid and is closer to the 1 cent per share offer from domestic player Air One, which lacked the deep pockets of its rival and was snubbed by Rome.
Air France-KLM also offered to pay 608 million euros to buy back Alitalia bonds and pledged to underwrite a 1 billion euro cash call to shareholders as part of a commercial overhaul.
It set a deadline of March 31 for several conditions on its offer, including agreement with airports operator SEA over a 1.25 billion euros claim for damages for cutting slots at Milan's Malpensa airport in half to 170.
The 138 million euro price for Alitalia stock is equivalent to roughly two days' of revenues at Franco-Dutch airline group Air France-KLM.
"This will give Alitalia the means to restart its development, and in consequence, consolidate its position as the national leader," Air France-KLM, itself founded from a merger of French and Dutch flag carriers in 2004, said in a statement.
The restructuring should return Alitalia to an operating profit -- which it has not posted since 1998 -- as early as 2009, the Franco-Dutch carrier said.
Alitalia has been on the block for more than a year as the Italian government unsuccessfully hunted for a buyer for its 49.9 percent stake. Rome will discuss the sale this week.
Though Air France-KLM has been considered a likely buyer for years, it snubbed an initial auction for Alitalia last year that failed, and expressed its interest only in December.
Alitalia bowed to the terms of the offer after a marathon board meeting that started on Saturday morning and continued into the early hours of Sunday.
Only part of Alitalia's troubled ground services unit, AZ Servizi, will be taken over by Air France-KLM -- signaling overall job losses could be higher than the 1,700 expected.
Alitalia's unions, who fear steep job cuts among AZ Servizi's 8,000 employees, attacked Air France-KLM for keeping them in the dark on expected job losses. One major union, Filt-Cgil, said it would never accept an offer that involves only a part of AZ Servizi being taken over.
"We have said many times that we will say yes only to an offer for the whole group: Alitalia and AZ Servizi," said union leader Mauro Rossi. "A logic in which one piece of the company is saved and the other thrown away will never find agreement."
Other Alitalia unions, such as those representing pilots, have been more favorable to a deal with the French carrier.
Just under half of the 8.7 million shares to be issued by Air France-KLM will go to the Rome government, implying an Italian government stake of 1.4 percent in Air France-KLM -- lower than a 3 percent previously reported.
Italy's government is expected to extend a credit line to Alitalia to allow the carrier to continue operations while the deal is completed and the capital hike carried out.
Alitalia has warned it needs a fresh cash infusion by mid-year to keep flying. It had a share market value of 746 million euros at Friday's closing price of 0.5383 euros.