He also wants Mr Barrow to carry everyone along in his task of taking Gambia to a new level.
The Nigerian leader made the demand in a telephone conversation with the President-elect on Monday shortly before his trip to the International Forum on Peace and Security in Senegal.
President Buhari again expressed his gladness at the conduct of the contestants before, during and after the elections.
He also expressed his admiration at the existing rapport between the President-elect and other contestants especially the current President, who lost the election.
A statement by a spokesman for President Buhari, Mr Garba Shehu, said the President observed that democracy, rule of law and respect for each other are fast taking roots in Africa and that Gambia had also become a role model for Africa and the world.
He further congratulated Mr Barrow again on his electoral victory.
The President had earlier congratulated him on Saturday December 3, after his triumph was announced.