There has been a high turnout at voting stations, reports say.
Opinion polls have put the governing Chama Cha Mapinduzi (CCM) party ahead, but the result is expected to be close.
Four opposition groups are backing one candidate, a former prime minister, in the presidential race.
The BBC’s Tulanana Bohela reports from the main city Dar es Salaam that usually busy streets and markets are deserted, and large queues have formed at polling stations as people wait patiently to cast their ballots.
President Jakaya Kikwete, who is standing down after two terms, has called for peace ahead of the election, adding that “anyone who tries to cause trouble will be dealt with”
CCM was formed in 1977 from a merger of two post-colonial parties and has effectively been in power since independence in 1961.
It has fielded Works Minister John Magufuli, 55, as its presidential candidate.
He is being challenged by Edward Lowassa, 62, who quit CCM after he failed to win its presidential nomination.
He is contesting the poll under the banner of the Ukwasa coalition.
The main presidential candidates:
John Magufuli – Chama Cha Mapinduzi
Aged 55, currently works minister
Promised change and to improve on the pace of progress laid down by the previous CCM government
Promised to end power shortages and exploit Tanzania’s natural gas discoveries
“My government will put emphasis on fighting corruption, job creation and industrialisation,” he said on Saturday
Nicknamed The Bulldozer for driving a programme to build roads across the country.
Edward Lowassa – Ukawa
Aged 62, left CCM when it did not pick him as its presidential candidate earlier this year
Four opposition parties rallied behind him as their joint candidate
“We must stop being a nation of beggars,” he told a rally on Saturday. “It is a shame for Tanzania to still be poor after 54 years of independence.”
Has served as prime minister, but resigned over corruption scandal in energy sector
Denies involvement in the scandal