The deal is expected to close in the first quarter of 2011, the two firms said in a statement, adding that the division would continue to operate as a stand-alone business under the Intel banner.
"The global demand for wireless solutions continues to grow at an extraordinary rate," said Intel boss Paul Otellini.
The transaction would allow Intel to boost its wireless offering, the executive added.
"As more devices compute and connect to the internet, we are committed to making certain that Intel is well positioned to take advantage of the growth potential in every computing segment, from laptops to handhelds," he said.
Infineon, which was slammed by the global downturn but has since rebounded strongly, said it was selling the group to concentrate on its core business.
"We all stand to benefit enormously from this deal," said Infineon chief executive Peter Bauer.
The move comes just over a week after Intel reached deep into its pockets to acquire Internet security firm McAfee for $7.68 billion.
Infineon shares rose slightly on the news as the DAX index of leading German shares opened in Frankfurt.