The comedian, real name Robert Nankeville, filed a civil action at the High Court in London last week against News Group Newspapers (NGN), the subsidiary of Rupert Murdoch's News International that published the News of the World until it closed down last July.
The lawsuit also names Glenn Mulcaire, the private investigator who was jailed in 2007 for intercepting voicemails on behalf of the paper.
Davro was a popular entertainer in the 1980s and '90s with a primetime Saturday night programme on ITV. He also appeared in BBC One soap EastEnders in 2007 and ITV's Dancing on Ice in 2010.
His former wife, ex-Page 3 model Trudi, is also taking legal action, as the couple were subjected to various lurid headlines in the tabloids in the early 2000s. They divorced in 2004.
They are part of a new round of civil lawsuits against News Group Newspapers after the publisher settled a number of cases earlier in the year, including Charlotte Church, Steve Coogan and Alastair Campbell.
David Beckham's father Ted filed legal papers against NGN at the High Court last month, joining Cherie Blair, TV personalities Jamie Theakston and Jeff Brazier, former boxer Chris Eubank, and footballers Peter Crouch, Kieron Dyer and Jermaine Jenas.
Mark Lewis, the lawyer representing various alleged phone hacking victims, recently told an Australian broadcaster that NGN could face up to 100 new lawsuits over phone hacking claims.
Lewis is also currently exploring options for launching legal action in the US on behalf of three people who allegedly had their phones hacked while on American soil, potentially causing even greater headaches for Murdoch's US-based News Corporation.
> The Times sued over alleged 'Nightjack' email hacking