"It is with great pleasure that I have just learned of my husband's release. For me and for my children it is the end of a nightmare that has lasted more than nine months," said Seigner, 44, who has two children with Polanski.
"I am really looking forward to being able to make plans and to once again have a normal family life, especially with my children, who did not deserve this suffering," the 44-year-old added in a statement.
The Swiss government said it would not extradite him due to a "fault" in the US extradition request relating to whether Polanski had already served his sentence in the United States and said it could not appeal the decision.
The director admitted plying 13-year-old Samatha Geimer with champagne and drugs during a 1977 photo shoot at the Hollywood home of actor Jack Nicholson before having sex with her despite her protests.
French Culture Minister Frederic Mitterrand said he was "delighted" for Polanski, a dual Franco-Polish citizen, saying his wife, children and friends "have supported him with dignity and determination throughout an ordeal in which the attacks deeply affected them."
Mitterand was one of the first public figures to defend Polanski shortly after he was arrested in September 2009 and many in French intellectual and cultural circles spoke out in favour of Polanski.
Foreign Minister Bernard Kouchner said in a statement that he too was "delighted by the decision," adding that he had called his Swiss counterpart to express his "deep relief".
Poland's Foreign Minister Radoslaw Sikorski thanked Swiss Foreign Minister Micheline Calmy-Rey in a phone conversation for the "prudent decision" to release Polanski, a dual French-Polish citizen.
"A solution was found which takes into consideration the complicated legal terms of this case and the life situation of Roman Polanski," a Polish foreign ministry statement said.
The United States at first stayed silent over the decision. "The department declines comment," was the only reaction from the Justice Department in a statement to AFP. But the US later said on Monday that it was "disappointed" with the decision.
But friends and colleagues in Poland and France welcomed Polanski's release.
In Paris, Polanski's French lawyer Georges Kiejman also hailed the Swiss decision and hoped the director would one day return to the United States.
"I pay tribute to Swiss justice, its judicial analysis is very correct," Kiejman told AFP.
One of Polanski's leading supporters in the case, the French writer-philosopher Bernard-Henri Levy who had launched a petition in his support, told AFP he was "mad with joy" at the decision.
"I just spoke to him. He feels the same as the millions of citizens who supported him," Levy said. "He feels that justice has been done."
In Warsaw, Jacek Bromski, head of Poland's film directors' association, said it was "very happy news, but there's also bitterness over the months of life taken from Roman."
Andrzej Serdiukow, the Polish co-producer of "The Pianist", for which Polanski won an Oscar, said it was a "great joy" for the director's friends as his morale had been low recently.
Polanski was born in Paris in 1933 into a Polish-Jewish family and moved to Poland in 1936 where he survived the Holocaust and made his first films before moving to France in 1961, then briefly to Britain and the US by 1968.
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