The deal, worth up to euro310 million (US$406 million), would be signed later in the day, the company said.
''The supervisory board of Deutsche Lufthansa AG in its meeting today has approved the business model developed jointly with Swiss International Air Lines AG for the takeover and integration of Swiss into the Lufthansa Group,'' the company said.
Shareholders representing 82.98 percent of Swiss shares had approved as well, the statement said.
As it announced the deal, the company also said that its board had extended CEO Wolfgang Mayrhuber's tenure by five years, until the end of 2010. His contract had been scheduled to run out at the end of this year.
Lufthansa said it would make an offer to smaller buy out smaller shareholders. Due to air traffic regulations and antitrust rules, Lufthansa said it would initially put Swiss shares into a new company called AirTrust, of which it would hold 11 percent.
Once antitrust approval is gained, the stake would be raised to 49 percent and after aviation regulatory approval, to 100 percent, the company said.
Swiss also said that Switzerland's government had given its approval to the deal.
Lufthansa said large shareholders of Swiss would get what it called an earn-out option, for which it would pay an aggregate euro265 million (US$347 million), and would spend some euro45 million (US$59 million) to buy out the free-float shareholders.
The company statement didn't provide a share price for its buyout offer.
EU Transport Commissioner Jacques Barrot has said he agrees in principle with a takeover. But the final decision lies with EU competition authorities.
Swiss has suffered massive financial problems since it was created out of the defunct Swissair in 2002. It has blamed its continuing financial problems on global economic instability, the SARS crisis in Asia, the Iraq war, high oil prices and competition from low-cost carriers in Europe.
Investment in the airline has been an expensive disaster for the country's major businesses, which were pressured by politicians to pump in cash after the collapse of the cherished Swissair.
The government and business put in more than 4 billion francs (US$3.4 billion; euro2.6 billion). Swiss has racked up aggregate losses of 2 billion francs (US$1.7 billion; euro1.3 billion).
Lufthansa shares rose 0.7 percent to euro11.16 (US$14.70) in Frankfurt trading. Swiss had suspended trading of its shares ''to prevent any uncertainty on the capital markets.''