During his speech in parliament on Thursday, ahead of the confidence vote, Godmanis spoke of the tasks ahead of his administration.
"Now that Latvia is a member of EU and Nato there are no new guiding posts. The nation must motivate itself on its way to a democratic, developed state with European living standards," he said.
Sandra Kalniete, a senior Latvian legislator and opposition politician, said the future government would have to tackle the issues of enforcing anti-corruption measures and the rule of law.
Kalniete was quoted by the AFP news agency as saying: "For Latvia, the crucial point is are we going to belong to the [transparent] Nordic political tradition or are we going to slide back?"
Aigars Kalvitis, the former prime minister, was forced to resign earlier this month after he fired Aleksejs Loskutovs, a popular anti-corruption investigator, sparking two large demonstrations and calls for the government's resignation.
Loskutovs was eventually reinstated, and Kalvitis's government, despite holding on to majority control in parliament, stepped down after a series of ministerial walkouts and public protests.
Many Latvians, including Valdis Zatlers, the president, had hoped that New Era, a popular opposition party, would join the new coalition.
But talks with the party broke down on Wednesday after New Era, unsatisfied with Godmanis, asked Zatlers to nominate an independent candidate as prime minister.
Godmanis, seen as Latvia's first "free" prime minster, previously served as head of government from 1990-1993 as the Baltic state gained its independence from the Soviet Union.