Jenkins, who scored 1,090 international points in his playing career, played an instrumental part in the Lions' 1997 series win in South Africa.
On that tour he scored 41 points in the three Tests to help the Lions win the series 2-1. Jenkins joins fellow countryman Robert Howley, and English men Andy Farrell and Graham Rowntree as assistant coaches.
Lions head coach Warren Gatland indicated late last year when naming his coaching staff that a further coaching appointment would be made closer to the tour.
Jenkins will perform the same role as he did on the 2009 tour to South Africa as technical kicking coach.
"Neil was one of the foremost kickers in the game, both out of the hand and in terms of goal kicking during his career. He has been working in the coaching environment in this crucial area with great success in recent years with Wales," he said.
"The tour to Australia will be one hell of a challenge and we need to ensure that our approach in all aspects of the game is first rate.
"Tactical kicking, when to kick, how to kick, and of course converting points through penalties and conversions is crucial to on-field success. Neil brings extensive knowledge to the squad in this area and the players can only benefit from this."
Jenkins commented: "It is a great honour to once again be part of a British & Irish Lions tour. I am delighted and grateful to have been offered this opportunity to join the 2013 coaching staff.
"As a player I was lucky enough to tour Australia with the Lions in 2001, it is a great country and they are one of the top teams in world rugby. Like 1997 it was a terrific series but unfortunately we lost 2-1.
"I have clear ideas of what I would like to contribute and I cannot wait to get out onto the training pitch and get started."
Eanna Falvey becomes the third Irishman to be appointed to the backroom staff of the 2013 British & Irish Lions, joining logistics officer Gerard Carmody and baggage master Patrick 'Rala' O'Reilly.
Eanna brings a specialist medical training to the position along with a wealth of experience in sports medicine and specifically in rugby, having worked at the highest level of the game.
He has been Ireland team doctor since 2009. As part of the IRFU medical structures, he previously worked as team doctor to the Ireland Under-21 international squad in 2005 and 2006 and the Churchill Cup side in 2008.
Dr. James Robson, Lions team doctor, said: "I am delighted to have Eanna on board. He joins a team with a wealth of previous Lions experience. I hope he enjoys the opportunity to be involved on such an amazing journey."
A medical graduate of University College Cork, Dr. Falvey was Munster team doctor between 2003 and 2007. During this time he also worked in hurling, Gaelic football, boxing and athletics.
As part of the IRFU medical structures, he also worked as team doctor to the Ireland Under-21 international squad in 2005 and 2006 and the Churchill Cup side in 2008 before becoming the Ireland team doctor in 2009.
His time ended with Munster Rugby in 2007 when he moved to Australia to complete his sports medicine training with a sports medicine research fellowship in the University of Melbourne, Olympic Park Sports Medicine Centre and with the medical team of Melbourne-based Australian Rules club Geelong.
Upon his return to Ireland, he joined the Sports Surgery Clinic in Dublin where he was appointed as the director of sports medicine.
A keen athlete himself, he is a former international amateur boxer and winner of Irish National Boxing Championships as well as being involved in competitive athletics.