A new poll of Republicans in Iowa puts Ms Bachmann on a par with frontrunner Mitt Romney A poll of party members there shows her virtually tied with frontrunner Mitt Romney, with 22% of the support.
Iowa is the first state Republicans vote in for their 2012 candidate.
Its caucuses in early February are the first electoral event in the US presidential nomination process.
BBC North America editor Mark Mardell says Republicans feel that next year's presidential election is winnable if only they have a candidate who sparkles - and Michele Bachmann is the latest to catch their eye.
She is already a darling of the Tea Party movement for her plain talking and forthright conviction politics.
While she has made her share of harsh statements - seen by opponents as gaffes - some think she has many of Sarah Palin's qualities with fewer of the drawbacks, our correspondent adds.
Ms Bachmann stresses her record as a tax lawyer and founder of a charter school, as well as repeating frequently that she is a mother of five children and foster mother to 23.
She is an economic conservative who says she will not vote to raise America's debt limit and is urging big tax cuts.
And Ms Bachmann is also a social conservative - a born-again Christian and a fierce opponent of abortion and gay marriage.
That goes down well with Republicans in Iowa, but may not be such a draw to those in the middle ground, our correspondent says.
Hours before formally announcing her bid, she spoke to hundreds of residents in her hometown of Waterloo, Iowa, and was quoted by Politico as saying: "Do you realise how powerful your vote will be? I need you. Will you help me?"
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