The abdication paves the way for the prime minister and longtime de facto ruler, Sheikh Sabah Al Ahmed Al Sabah, to become the country's new emir.
"An agreement has been reached in the family and he will sign the abdication papers tomorrow," parliamentarian Nasser al-Saneh told The Associated Press.
He said the two struggling camps of the family met on Monday evening to reach a compromise before a parliament session that was to debate Cabinet demands that the ailing new emir be ousted in favour of the Sheikh Sabah.
A swearing-in ceremony for Sheikh Saad had been planned for Tuesday evening.
Sheikh Sabah, the prime minister, has been running the day-to-day affairs of the country since the late emir, Sheikh Jaber Al Ahmed Al Sabah, and his successor and the then-crown prince, Sheikh Saad, both fell ill.
Both Sheikh Saad and Sheikh Sabah are in their mid-70s - their exact ages are not known - but Sheikh Sabah is the more fit of the two. He had a heart pacemaker implanted but otherwise is said to be in good health
The leadership crisis began coming to a head on Friday when scores of ruling family members visited Sheikh 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 emir.
The push for Sheikh Sabah's ascension, however, was snarled when some members of Sheikh Saad's branch of the ruling family objected. Key among them was Sheikh 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.