Coe, twice an Olympic 1,500 metres champion who won his first gold at the 1980 Moscow Games and was appointed the chairman of the 2012 Games, will go for election when current BOA head Colin Moynihan, in charge since 2005, steps down later this year, with a vote likely in November.
Moynihan announced after the Olympic Games in August that he would hand over to a replacement to give them time to settle in before the 2014 Sochi Winter Olympics.
"I am happy for my name go to forward. I was asked formally and on this day of all days why wouldn't you want to help?" Coe told reporters on Monday following a London parade to laud the efforts of the British Olympians and Paralympians.
"I wouldn't presume anything but I was asked, I thought about it, and I have always had a huge debt of gratitude to the British Olympic Association."
Coe said his participation in Russia in 1980 had been thanks to the BOA, who also gave the middle-distance runner a berth at the 1984 Los Angeles Games despite a battle with illness.
"They fought to allow me to go to Moscow and actually everything I have done in the last few years might not have been possible had I not had that Olympic experience.
"So it's an organisation I have a deep, deep commitment to. The BOA is a fantastic organisation."
Coe helped to secure the Games for London in 2005, a move which had its doubters.
Britain's Olympians notched up 29 golds on their way to their biggest haul of 65 medals in more than a century while the Paralympians' tally of 120 medals was their best since Sydney in 2000. Huge and enthusiastic crowds packed venues during the Games.
Coe has also expressed interest in running for the presidency of the International Association of Athletics Federations after Senegal's Lamine Diack leaves the post in 2015.
Coe was appointed by Prime Minister David Cameron as Olympic legacy ambassador following the closure of the July 27-August 12 Olympic Games and is a former Conservative member of Parliament.
He will advise Cameron on how best to secure the long-term benefits of hosting the Games as a roving ambassador to help win new trade and investment deals for British businesses.