Nigeria's leaders were often the target of Achebe's writing and the author rejected national awards in 2004 and 2011, but Jonathan paid tribute to him and argued that the country was changing.
"All of us must work together so that our children will know there is a country," Jonathan said at the service, a reference to Achebe's last book, "There Was A Country".
A number of women mourners wore purple headwraps and white dresses, while some men dressed in traditional shirts adorned with Achebe's picture.
Access inside the Anglican church was invitation-only, but several thousand people flocked to tents with loudspeakers outside or to surrounding streets, where two giant screens were set up.
"I left my house in Asaba (a nearby city) at 5:00 am this morning in order to pay my last respects for this illustrious son of Nigeria who has done his people proud," said 31-year-old engineer Sylvanus John.
Groups of admirers could be seen dancing and singing in praise of Achebe in the Igbo language spoken throughout the region.
After the church service, he was buried in a mausoleum on the family compound in a private ceremony.
Achebe, who died in the United States in March aged 82, is viewed as an iconic figure in Nigeria and abroad, and his death led to tributes worldwide.
Ogidi, in Nigeria's Anambra state, was decorated with posters of Achebe, while police were stationed throughout the town.
"The death of my uncle is indeed a great loss not only to the family but to Nigeria and Africa as a whole," 64-year-old Obi Achebe said.
"He has left big shoes that will be difficult to be worn by anybody."
Achebe had lived and worked as a professor in the United States in recent years, most recently at Brown University in Rhode Island. A 1990 car accident left him in a wheelchair and limited his travel.
Nigeria's Guardian newspaper on Wednesday dedicated an entire page to a poem written for Achebe by Wole Soyinka, the Nigerian writer and Nobel literature laureate.
While he was known worldwide mostly for "Things Fall Apart," a novel about the collision of British colonialism and his native Igbo culture in southeastern Nigeria, Achebe also wrote non-fiction that tackled his country's problems.
Africa's most populous nation and largest oil producer remains severely underdeveloped, held back by corruption and mismanagement.
Achebe's work earned him praise from some of the world's most respected leaders, including Nelson Mandela, who described him as a writer "in whose company the prison walls fell down".
South African writer and Nobel laureate Nadine Gordimer called Achebe the "father of modern African literature" in 2007, when she was among the judges to award him the Man Booker International prize for fiction.
Achebe also strongly backed his native Biafra, which declared independence from Nigeria in 1967, sparking a civil war that killed around one million people and only ended in 1970.
The conflict was the subject of a long-awaited memoir published last year, titled "There Was A Country: A Personal History of Biafra."
"Things Fall Apart" -- his first novel -- was published in 1958. The novel, which traces an Igbo tribesman's fatal brush with British colonialists, has sold more than 10 million copies worldwide and has been translated into 50 languages.
The Guardian in Britain wrote in 2007 that the novel "turned the west's perception of Africa on its head -- a perception that until then had been based solely on the views of white colonialists ..."
It has become required reading at many universities, and Achebe is credited with profoundly influencing a generation of Nigerian writers who followed him.