Coe, who succeeds Lord Moynihan as chairman, was elected unopposed for a four-year term after his only rival, British Hockey chief Richard Leman, withdrew last month.
“Following the tremendous impact of the London 2012 Games, the BOA has an important role to play in ensuring the growth of the Olympic movement throughout the UK and the continued success and support of Team GB at future Olympic Games,” said Coe.
Former gold medal-winning athlete Coe led London’s bid to host the Olympics and then ran the organising committee for the event itself, which was widely hailed as one of the greatest of all time.
Prime Minister David Cameron, who in August appointed Coe legacy ambassador, welcomed the former Conservative MP’s latest role.
He said: “Seb Coe demonstrated inspirational leadership in delivering the best ever Olympic and Paralympic Games this summer and as a double Olympic gold medallist himself there can be no better choice for BOA chairman.”