Mr Yatsenyuk, in office since former pro-Russian President Viktor Yanukovych was ousted in February 2014, said he would inform parliament on Tuesday.
The current President, Petro Poroshenko, asked him to quit in February, saying he had lost support.
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.
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