The 30-year-old becomes Blues second signing during the January transfer window, with defender Ferdinand Coly signing from French club Lens.
“We are delighted that he has chosen us. To have someone with his credentials is a massive, massive thing for us,” said Blues boss Steve Bruce.
“Once I had met him – two weeks ago – he shook my hand then and said he would like to come. He has been true to his word.
“It is the biggest signing this club has ever made.
“Fifty-five caps for France over the last decade shows magnitude. He is a World Cup winner and has played for Barcelona and AC Milan.
“I think he will be a great favourite. He wears his heart on his sleeve and his talent will not go unnoticed,” Bruce told Sky Sports News.
“I spoke to Patrick Vieira, Robert Pires and Laurent Blanc and they told me it was the championship for me. They told me to sign as quick as I could,” said Dugarry.
“I am very happy, for me it is a good thing. I would like to play in the Premiership and after discussions with Steve Bruce I was sure it was the club for me."
“Everything I see I am happy with. I don’t care to sign for the image. The most important thing for me was to be sure people are expecting something from me.”
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