Macri's argument with Fernandez stemmed from his wish that he receive the presidential sash and ceremonial baton at the palace, while Fernandez insisted on holding the full ceremony in Congress, where her party has the most seats.
They also aligned Argentina with socialist leaders like the late Venezuelan President Hugo Chavez and Bolivian President Evo Morales, who attended Fernandez's farewell speech.
In his Thursday address, Macri promised to fight the nation's growing drug trade "as no president has before". Argentina has the potential to be both a regional and global energy leader, but after 12 years of Kirchnerismo, Macri has a long road ahead.
In this Friday, Dec. 4, 2015 photo, Argentina's President-elect Mauricio Macri walks down an inner ramp of the Planalto Presidential Palace, after meeting with Brazil's President Dilma Rousseff, in Brasilia, Brazil.
Mauricio Macri who's twice been elected President of Boca Juniors soccer club and was Mayor of Buenas Aires, has now got the top job.
Earlier, Macri greeted his supporters from the balcony of her house, accompanied by his wife, Juliana Awada and their daugther Antonia, and then headed to the Congress along the traditional De Mayo avenue.
Ms Fernandez is to skip Thursday's swearing-in after the two became embroiled in a row over the ceremony's location.
He obtained an injunction from a judge ruling that her term ended at midnight on Wednesday, rather than at midday on Thursday, meaning that she would have no official authority over the ceremony.
The court ruled in his favor, deciding that the country would have three presidents in a matter of hours: Kirchner until midnight, incoming Senate speaker Federico Pinedo until the inauguration ceremony, and Macri thereafter.
Macri's victory is seen by many as an end to those policies.
In his inaugural speech, Mr Macri is likely to call for reconciliation and unity.
Mr. Macri's advisers also said his administration will cut income taxes for lower-to-middle-income workers, seeking to boost consumer spending before a devaluation that is widely expected to accompany the elimination of currency controls.
"We believe in that which we've attained so we must truly have a favorable approach to make sure that these matters WOn't be ruined", she said.
"When you feel that those who you trusted and voted for have betrayed you, take up your flags", she added.
Fernandez is revered by many Argentines for expanding welfare benefits, nationalizing some companies and introducing new civil rights like gay marriage.
Macri has promised to end the previous Peronist government's interventionist policies and open up Latin America's third largest economy to spur growth.
BUENOS AIRES, Argentina (AP) - Argentina's outgoing president is facing criticism for deciding not to attend her successor's inauguration.