Ahmad Baqir, the Kuwaiti justice minister, told Reuters on Tuesday an official letter with the nomination would be sent to parliament on Wednesday.
If confirmed by parliament, Shaikh Sabah, who as prime minister has been de facto ruler of Kuwait for the past four years, will officially replace the ailing amir, Shaikh Saad al-Abdulla al-Sabah.
Earlier on Tuesday, according to Jasim al-Khurafi, the assembly speaker, the Kuwaiti parliament unanimously voted to remove Shaikh Saad due to his poor health. He had become amir on 15 January.
The vote was taken shortly before the house received an abdication letter from the amir, parliamentarians said.
"After listening to the medical report [on Shaikh Saad's health], the assembly with its 65 members agreed to remove him from the post of amir," al-Khurafi said. He said that the cabinet would run the country until a new amir was named.
Shaikh Sabah has the support of many in the ruling family, but by becoming amir he would interrupt a long tradition of alternating power between the two branches of the al-Sabah dynasty.
Both Shaikh Saad and Shaikh Sabah are in their mid-70s - their exact ages are not known - but Shaikh Sabah is the more fit of the two.
Shaikh Sabah is now set to
become the new amir of Kuwait
He had a heart pacemaker implanted, but otherwise is said to be in good health.
The leadership crisis reached a climax on Friday when scores of ruling family members visited Shaikh Sabah at his residence and asked him to take charge of the country.
He accepted the draft, which was widely seen as approval of his becoming amir.
The push for Shaikh Sabah's ascension, however, was snarled when some members of Shaikh Saad's branch of the ruling family objected.
Key among them was Shaikh Salem al-Ali al-Sabah, chief of the National Guard and the oldest member of the family. His status of family elder added particular weight to his objection.