The Archbishop gave the advice in a statement made to the News Agency of Nigeria in the capital city, Lagos.
He asked the President-elect to stick to the road-map his party had laid: "It is heartening to know that he has made anti-corruption campaign the metier of his administration.
"In order for this not to run out of steam, he must build institutions, both formal and informal, that will fight corruption and ensure Nigeria becomes a society of law abiding citizens.
"His transition team and board of advisers should shun the temptation to secure their selfish interest and come up with pragmatic action plan that will help the president-elect realise his goal."
The cleric said the President had a large task ahead of him and asked that he explore economic and social opportunities in rebuilding the nation.
Buhari's Vice President, Mr Osinbajo, is a Christian and will be working with a Muslim President.
The Archbishop added that "the Gen. Buhari-led government must run an inclusive government of credible people with requisite competence that will ensure that no part of the country is left behind.
"He must ensure that no group, class, gender or religion is discriminated against politically, economically, socially and infrastructurally.
"This is the watershed moment to break the walls of ethnicity, elitism and religious bigotry that has continued to polarise the fragile unity of our nation.
"He has a duty to turn the nation into a bridge in which every person, irrespective of his background and orientation, would see the state as a collaborator and an ally through which his dreams and ambitions can be realised."
Revd Okogie also stressed that change is a gradual process.
"Nigeria seems to be on a collision course with destiny and the hopes of many are hanging in the balance. I can understand the sense of urgency and expediency in the expectations of Nigerians.
"Yet sincerely, I think we are expecting too much too soon. Change will come but it will be gradual but surely.
"It will amount to putting the cart before the horse to expect radical revolution from the General.
"We must exercise patience and give him chance to deliver on his promises. What he needs more than anything is our support, cooperation, collaboration and goodwill."