Moynihan steps down as BOA chairman on Wednesday after seven years in the role with London 2012 chairman Coe - who has been voted in unopposed - taking over.
The pair did not see eye-to-eye in the build up to the home Games this summer, with disagreements over the Joint Marketing Agreement for the Games and the funding of the Paralympics.
Moynihan however believes such disagreements were to be expected and are now water under the bridge.
And the outgoing chief is also adamant that, in Coe, the BOA will have the global punch to emerge from any post-Olympic funding and sponsorship lull in fine fettle.
"Seb will do an outstanding job," Moynihan said. "The fact that he is keen to do it is an endorsement of the position the BOA now holds in British sport.
"Seb can add value in a wide range of areas because he has a very high national and international reputation as an outstanding leader in sports administration.
"The reputation he has rightly gained from a great Games this summer will benefit the BOA. He will add particular value through the many sponsorship deals which we are already negotiating.
"I think we are right to hold back on announcing those so that Seb can be the driving force behind them. They are, after all, sponsorship deals for the next four to eight years and they are coming along well.
"I also think the three key objectives which I have sought to deliver in my time - namely being athlete-centred, performance driven and professionally managed - are all criteria that Seb strongly believes in and will wish to take forward.
"So on all those fronts, I think he will be a strong chair with my complete support at all times.
"My challenge was to see how we could move forward to Beijing and London. Seb now has the challenge to build on London and to deliver in Rio and beyond."