Kidney, who led Munster to Heineken Cup finals in 2000 and 2002, replaces new Wales coach Mike Ruddock at the Gwent regional side.
Dragons captain and former Wales centre Andy Marinos has been appointed as the new chief executive at Rodney Parade in place of David Jenkins.
Kidney takes the post in preference to an Ireland Rugby Football Union offer. They wanted him to look after Ireland's Elite Youth programme.
Kidney will be take the helm at Rodney Parade.