His government has been accused of inaction and corruption.
The International Monetary Fund (IMF) has threatened to withhold aid money if it does not carry out reforms.
Parliamentary Speaker Volodymyr Groysman has been nominated by Mr Poroshenko’s party to replace Mr Yatsenyuk.
Announcing his resignation on Twitter, Mr Yatsenyuk called for the formation of a new government immediately to prevent “destabilization of [the] executive branch during a war”.
The government in Kiev is signed up to an uneasy truce with pro-Russian rebels in two of Ukraine’s eastern regions, with frequent ceasefire violations reported.
Russia itself annexed the southern region of Crimea two years ago after a controversial referendum on self-determination.
US Vice-President Joe Biden, in a call to Mr Yatsenyuk on Sunday, congratulated him on “accomplishments over the past two years”, including economic reforms, but said “these changes must be irreversible”.
Poroshenko’s chance: Analysis by Tom Burridge, BBC News, Lviv
Arseniy Yatsenyuk’s resignation comes as no surprise. According to opinion polls, his party’s popularity had plummeted and he narrowly survived a vote of no confidence in parliament in February.
President Petro Poroshenko could now consolidate his power if he can install Volodymyr Groysman, a member of his own party, as the next prime minister.
Mr Poroshenko and a new government will be under intense pressure, both from Ukraine’s European and American partners, and the Ukrainian people, to implement real reform.
Several high-profile reformers have left the government in recent weeks, claiming it was failing to tackle corruption.
“As of today,” Mr Yatsenyuk tweeted on Sunday, “my goals are broader: new electoral law, Constitutional reform, Judicial reform, Ukraine’s membership in the EU and NATO.”
Ukraine’s EU ambitions suffered a setback on 6 April when voters in the Netherlands roundly rejected a landmark EU trade deal with the former Soviet state in a referendum.
Mr Yatsenyuk came to power promising to tackle corruption and implement economic reforms but has increasingly become the focus of accusations of corruption, even though no concrete evidence was produced.
Western governments have expressed concern over the resignation of reform-minded figures from the government.