The NDC complained about irregularities in voting in the first round, which had a turnout of around 70 per cent.
However, the EU's election monitoring team hailed the poll as a credit to African democracy, which sorely needs a boost after electoral chaos in Kenya and Zimbabwe and coups in Mauritania and Guinea this year.
The run-off is expected to be a close-fought affair, with both candidates in with a strong chance of victory.
The NPP lost its parliamentary majority in elections held at the same time as the first round of the presidential poll.
Atta Mills and Akufo-Addoe are vying to replace John Kufuor, who must step down in January after serving two terms.