City's website said the 32-year-old Given, the Republic of Ireland's first choice keeper, had joined for an undisclosed fee after passing a medical on Sunday.
"I have said for a long time that we need the experience of a keeper like Shay," City manager Mark Hughes said on the Premier League club's website.
"I am delighted that we have been able to acquire such an accomplished keeper, and one is so highly regarded by everyone in the Premier League."
City, the big movers in the January transfer market thanks to a takeover by an Abu Dhabi-based group last year, have also signed Craig Bellamy from West Ham United, Wayne Bridge from Chelsea and Dutch midfielder Nigel de Jong from Hamburg.
They also failed with an audacious attempt to sign Brazilian Kaka from Italian club AC Milan for a fee reported to be in the region of 100 million pounds ($143.1 million).
"I have had a good talk with (Shay) about where we expect to be in the future," Hughes, whose side are still not safe from relegation this season, said.
"From a football point of view, and a club point of view, it's an easy thing to sell because we know we are going in the right direction. Players want to be part of that."
Given made more than 450 appearances for Newcastle.
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