Inter Milan owner Massimo Moratti announced Tuesday that the deal was being finalized.
Juventus, which said in a statement to the Italian stock exchange that Inter would pay for the transfer over three years, paid Arsenal Ђ 18.1 million (US$23.1 million) for Vieira only one season ago.
Juventus was demoted to Serie B and stripped of its last two titles in Italy's match-fixing scandal. Third-place Inter was named as Serie A champion last week as the highest-ranking team not implicated in the scandal, the AP reports.
Juventus has already lost Gianluca Zambrotta, Lilian Thuram, Emerson and Fabio Cannavaro.
Defenders Zambrotta and Thuram moved to FC Barcelona. Midfielder Emerson and defender Cannavaro linked up with former Juventus coach Fabio Capello at Real Madrid.