Last December Mills was elected in a peaceful, transparent vote that set an example for the continent.
Obama was due to deliver a keynote speech at parliament on Saturday before visiting Cape Coast Castle, a fort used in the transatlantic slave trade.
Al Jazeera's Yvonne Ndege, reporting from Accra, said the countdown to the speech had begun and that there was a "great deal of excitement amongst Ghanaians but a sense of nervousness among leaders all over Africa".
"President Obama will criticise the way many African countries have been run. He'll say it's time to stop making excuses," she said.
"He has chosen Ghana because he wants to hold Ghana up as an example of a country that is run democratically; that has sound economic management. There has been a huge amount of discussion across Africa about why he chose Ghana.
"It doesn't have the biggest population in Africa; it is not the richest country in Africa but it does have a sound democratic system ... What people are expecting Obama to speak on is the fact that democracy is linked to prosperity in Africa."
Ghana, a cocoa- and gold-producing country, is set to begin pumping oil next year and has embarked on economic reforms that have helped bring unprecedented investment and growth.
Bunmi Akpata-Ohohe, of the London-based Africa Today
magazine, told Al Jazeera that as US president Obama could "only do so much" for Ghana and Africa.
"Obama is not a messiah; Obama is only on the agenda of America. He is only an American president," she said.
The visit of Obama and his wife Michelle will last less than 24 hours before they return to the United States.'Significant growth'
Before leaving for Ghana after the G8 summit in Italy, Obama said: "Part of the reason that we're travelling to Ghana is because you've got there a functioning democracy, a president who's serious about reducing corruption, and you've seen significant economic growth."
"My father travelled to the United States a mere 50 years ago and yet now I have family members who live in villages - they themselves are not going hungry, but live in villages where hunger is real," he said.
"If you talk to people on the ground in Africa, certainly in Kenya, they will say that part of the issue here is the institutions aren't working for ordinary people. And so governance is a vital concern that has to be addressed."
John Kufuor, a former Ghanaian president, told Al Jazeera that Obama was "coming to Ghana as a beacon of good governance [and] democratic practice".
|Ghanaians have been celebrating the first visit of the first US black president to Africa [AFP]
"He wants to come here so as to encourage other countries in Africa to go in the direction of Ghana,” he said.
Thousands of Ghanaians packed the dark streets around the airport, hoping for a glimpse of Obama.
"It's a great moment for Ghana and Africa. We have to celebrate our own," said driver Emmanuel Tsawe, who covered his 43-seater bus with Obama posters.
"I believe he has good intentions for the continent and we must co-operate with him," he said.
The authorities in Cape Coast, which lies about 160km west of the capital, have suspended funerals in the run-up to Obama's visit to a castle in the town that was once used as a slave trading post.
"The dead can be buried later," said Ama Benyiwaa Doe, Ghana's central regional minister.
"We banned all funeral activities in Cape Coast because we want to give a befitting welcome to the US president.
"Obama is here for once and we must pay all attention to him."