Conservative-backed independent Ingrida Simonyte -- an ex-finance minister who oversaw biting austerity cuts during the financial crisis -- narrowly won the first round on 12 May against fellow economist Gitanas Nauseda, also running as an independent in his first bid for public office.
Simonyte scored 31.13 percent ahead of 30.95 percent for Nauseda, who has since won the support of the governing Farmers and Greens Union after its candidate, Prime Minister Saulius Skvernelis, came third in round one with 19.72 percent.
No opinion polls were published before Sunday's vote coinciding with European parliament elections, but analysts expect Nauseda to prevail due to his independence, broad political appeal and personality.
The winner will replace incumbent President Dalia Grybauskaite, a 63-year-old independent who cannot run for a third consecutive term.
Dubbed the "Iron Lady" for her hard line on Russia, Grybauskaite is tipped as a possible president of the next European Council.