Eddie O'Sullivan has been included on the coaching ticket along with Andy Robinson, Ian McGeechan, Phil Larder, Gareth Jenkins and Mike Ford.
It is expected that the coaching team will be formed into two groups with O'Sullivan, Robinson and Larder taking the test side and McGeechan, Jenkins and Ford taking the midweek team.
Other Irishmen included in the 26-strong group are Gary O'Driscoll (Doctor), Dave McHugh (Specialist Advisor) and John Feehan (Chief Executive).
"We have got the right management group behind the team, that is one of the key factors in ensuring that the Lions can deliver our ultimate aim of winning the Test series," said Woodward.
"Whether on the coaching, medical, fitness, media, logistics or legal side of things, it is about creating the right blend and a support structure to give us the best opportunity to be successful in New Zealand."
British and Irish Lions Management Team:Sir Clive Woodward (head coach), Bill Beaumont (tour manager), Andy Robinson (coach), Eddie O'Sullivan (coach), Phil Larder (coach), Ian McGeechan (coach), Gareth Jenkins (coach), Mike Ford (coach), John Feehan (chief executive), Louise Ramsay (team manager), Dave Alred (specialist coach), Dave Reddin (fitness coach), Craig White (fitness coach), Tony Biscombe (video analyst), Gavin Scott (video analyst), James Robson (head doctor), Gary O'Driscoll (doctor), Phil Pask (physiotherapist), Bob Stewart (physiotherapist/masseur), Stuart Barton (physiotherapist/masseur), Richard Wegrzyk (masseur), Dave Campbell (chef), Dave Tennison (kit technician), Louisa Cheetham (media liaison), David McHugh (specialist advisor), Richard Smith (legal support).