There have been reported disputes over cabinet positions behind the scenes.
But politicians in Mr Poroshenko`s coalition say they now have enough members for a wafer-thin majority.
Oleksiy Honcharenko told Interfax news agency there was a coalition of 226 out of the 450-member parliament.
"The president has said he is ready to immediately submit to the parliament Groysman`s nomination for the post of prime minister, and we will immediately vote for it," the MP said.
"This all is going to happen today."
Separately, the deputy speaker of parliament, Andriy Parubiy, told Reuters that four independent MPs had joined Mr Poroshenko`s faction, enough to form a majority.
Reports had emerged late on Monday that Mr Groysman would not take up the post amid disagreements over the new cabinet.
Negotiations are continuing ahead of the parliamentary vote and it is not clear yet how the disagreements have been resolved.
The BBC`s Tom Burridge in Ukraine says that if there is no progress towards the creation of a stable reform-minded government, there will be frustration in Berlin and Washington, and satisfaction in Moscow.
The Western-backed reform programme of the government has stalled in recent weeks and several high-profile reformists have left the government.
Economy Minister Aivaras Abromavicius resigned more than two months ago after accusing the government of lacking commitment to end corruption.
Long list of problems
Mr Yatsenyuk has been in office since former pro-Russian President Viktor Yanukovych was ousted during huge demonstrations in February 2014.
Announcing his resignation on Sunday, Mr Yatsenyuk accused Ukraine`s politicians of failing to enact "real changes".
His loss of parliamentary support led to him being asked by President Poroshenko to resign in February. Although he survived a vote of confidence he remained unpopular in opinion polls.
The International Monetary Fund has threatened to withhold aid money if Ukraine does not carry out reforms.
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 annexed the southern region of Crimea two years ago after a controversial referendum on self-determination.
Ukraine`s ambitions to join the EU also 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.