The council re-elected former England captain Bill Beaumont for a second term as IRB vice chairman, while a new executive committee was also elected.
Lapasset was a key figure behind the France 2007 bid and in his capacity of chairman of the organising committee, he has played an instrumental part in the delivery of the most successful World Cup in history. He will serve a minimum four-year term, with his chairmanship starting on January 1 next.
He said: "I am honoured to be following such a figurehead who has played, coached and administered the game at the highest level. I would like to thank Dr. Syd Millar for his extremely important contribution for the development of the game.
"He has managed to adapt the IRB strategic plan to the realities of today's game and he has modernised the organisation's governance and management structures.
"The game has never been in such good health. The global success of the 2007 World Cup has put rugby very much in the forefront of people's minds and it is important that we continue to capitalise on that success," added Lapasset.
Millar, who made 37 Test appearances for Ireland between 1958 and 1970, will be remembered as one of the game's great administrators. He represented Ireland as a player, coach and manager, and was elected President of the Irish Rugby Football Union in 1995 after 10 years of service.
He served on the Six Nations Committee and was also chairman of the British & Irish Lions from 1999 to 2002. Millar joined the IRB Council as an Irish delegate in 1994 and served in that position until taking over the role of interim chairman after the death of Vernon Pugh QC in 2002.
Elected chairman in November 2003, Millar presided over the modernisation of the IRB, including a new governance structure and the implementation of the existing strategic plan.
"I leave the position of IRB chairman with nothing but wonderful memories. I have thoroughly enjoyed the role and my time at the IRB, have made many friends and am confident that the global game is in excellent hands," said the 73-year-old Ballymena man.
The IRB Executive Committee was also elected and comprises of - Bernard Lapasset (IRB chairman), Bill Beaumont (IRB vice chairman), Mike Miller (IRB chief executive officer), Oregan Hoskins (South Africa), David Pickering (Wales), Bill Nolan (Scotland), Peter Boyle (Ireland), Graham Mourie (New Zealand), Paul McLean (Australia) and Carlos Tozzi (Argentina).