Adverts for the Falcon 7X executive jet and Hawker 4000 are to appear in newspapers, Garba Shehu said.
Some of the other presidential aircraft are be handed to the Nigerian air force to boost its operations, he said.
The country is one of Africa's leading economies but it is now suffering from its worst economic crisis in years.
In a Facebook post, Mr Shehu said the downsizing of the president fleet had been a campaign promise made by Mr Buhari before his election last year.
The president had requested a compact and reliable aircraft for transporting government officials on special missions, he said.
"This exercise is by no means complete," the spokesman added.
BBC Abuja bureau editor Naziru Mikailu says the advert for the jets will ask potential buyers to bid in US dollars, not the local naira currency.
Nigeria's economy slipped into recession in August.
The government depends on oil sales for about 70% of its revenues - and the slump in global oil prices has hit the West African nation hard.
A planned luxury 4bn rand (Â£185m) aircraft for South Africa's Jacob Zuma was widely criticised last year as were plans by Swaziland's King Mswati to acquire a second private plane. By contrast, former Malawian President Joyce Banda was widely praised when she auctioned her official jet in 2013 and vowed to hitch rides with other leaders.
The need for a US presidential jet, nicknamed Air Force One, is rarely questioned.
But not every country has a private jet for their leader.
The first jet for a British prime minister was inaugurated in July. The UK had been the only country in the G20 group of the world's major economies not to have one.
Nigeria is selling two of its 10 presidential jets in a bid to "cut down on waste", President Muhammadu Buhari's spokesman has said.