Buhari delivered the lines at the launch of a landmark campaign on September 8, unaware that part of his speech was lifted.
Buhari in his speech for the "Change Begins With Me" campaign, said, "We must resist the temptation to fall back on the same partisanship, pettiness and immaturity that have poisoned our country for so long."
The line was taken verbatim from Obama's speech, which he gave eight years ago after his victory over Arizona Sen. John McCain.
The incident was particularly embarrassing for the president because "Change Begins With Me" is a flagship policy meant to demand honesty and integrity from Nigerians.
Presidential spokesman Garba Shehu confirmed to CNN that the unnamed civil servant had been relieved of his duties at the state house.
He said: "He came from the Office of the Head of the Civil Service on posting and he was asked to return (to that office). They will handle his case in accordance with their regulations."
At the time, Shehu blamed the error on "overzealous administration staff." "We regret that this has happened. This serious oversight will be investigated thoroughly and appropriate punishment meted."
The presidency has put in place digital software used by editors to combat plagiarism, the spokesman said.
It is not the first time Buhari has been called out for plagiarism. In his inauguration speech in May 2015, he received plaudits for his quote: "I belong to everybody and I belong to nobody."
This line was later attributed to French President Charles de Gaulle, who was quoted in a book saying, "I am a man who belongs to no one and who belongs to everyone," while addressing a press conference on May 19, 1958.
Buhari's "Change Begins With Me" campaign, which includes a push against widespread corruption, has proved somewhat ill-fated, with some Nigerians criticizing it for being tone-deaf and failing to address their needs during a biting recession. Many took to Twitter to vent against the campaign
Speaking at its launch, Buhari said: "The campaign principle is simple, each of us must live the change we want to see in our society. Before you ask, 'where is the change they promised us,' you must first ask, 'how far have I changed my ways."