Two separate exit polls showed Iohannis garnered 64%-67% of the vote, with former prime minister Viorica Dancila of the left-leaning PSD taking 33-36%.
"The winner today is modern Romania, European Romania, the normal Romania," Iohannis told reporters in his victory speech.
Under a succession of PSD governments, Romania, a European Union member state, has rolled back anti-corruption measures in recent years. Along with ex-communist peers Poland and Hungary, it has been heavily criticised by Brussels for its actions.
However, 60-year-old Iohannis has been credited by Western allies and the European Union with trying to protect the rule of law, in particular by challenging attempts to limit judges' independence.
The president's powers are mostly limited to nominating a prime minister on the basis of who can command a majority, challenging laws in the Constitutional Court, and appointing some chief prosecutors.
Iohannis is expected to install anti-graft and anti-mafia prosecutors who are serious about tackling endemic corruption with the backing of Prime Minister Ludovic Orban, who became head of a liberal minority government by winning a parliamentary vote of confidence three weeks ago.
Teacher Andreea Mihai, 50, said "things should slowly return to normality. Both Orban and Iohannis will work together in the same direction."
Dancila's PSD had increased the burden of proof in corruption cases, reorganised panels of judges and set up a special unit to investigate magistrates for potential abuses, a move widely seen as an instrument of political coercion.
Romania's judicial reforms have been monitored by Brussels since it joined the EU in 2007; in October, Brussels said the reforms were going backwards.
Iohannis, a soft-spoken ethnic German and former mayor of Sibiu, became president in 2014.
He helped to secure popular approval in a referendum last May that called for the government to be banned from altering legislation by emergency decrees, and advocated a ban on amnesties and pardons for graft-related crimes.
Data from Romania's election commission, which is expected to announce partial official results on Monday, showed turnout of about 50%, with a record 920,000 voters from the country's diaspora taking part.