Africa's biggest copper producer voted on Thursday to choose a successor to Levy Mwanawasa, who died in August after suffering a stroke.
Sata has accused the ruling party of rigging the vote.
The country's largest independent election monitoring group said on Friday the election has been generally peaceful, but there were some instances of voting irregularities.
The winner faces the formidable task of matching Mwanawasa's strong record of fiscal discipline, praised by Western donors, and of cracking down on corruption, two rare successes in Africa.
|Banda promises to carry on programmes
of Mwanawasa, the late president [AFP]
Mwanawasa's business-friendly policies saw foreign investment in Zambia soar from $71.7m in 2001 to an estimated $4bn in 2008, with $1bn of that coming from China.
The late president won international praise for fighting corruption and modernising the economy, but had admitted failure in lifting the nation out of crushing poverty.
Banda, a prominent businessman with wide government experience, has campaigned as a steady hand who can keep Mwanawasa's business-friendly policies going.
"I will continue the policies and programmes that Mwanawasa started. I will complete them and add more," Banda told supporters during his campaign.
Sata portrays himself as a champion of the poor. About 65 per cent of Zambia's 12 million people live on less than $1 a day.
Although the vote is seen as a test of Zambia's commitment to multi-party democracy, restored in 1990 after 18 years of one-party rule under Kenneth Kaunda, neither Banda nor Sata is expected to reshape the political landscape dramatically.