On Thursday, a panel of three judges removed the orders preventing Kindiki’s swearing-in, ruling that an extended vacancy in the office of deputy president was “untenable”.
The court cited the need for continuity in the office of the second-in-command in the country.
Gachagua’s lawyers say they will appeal against the judges’ ruling.
But the court also said that the case challenging Gachagua’s impeachment itself can continue.
During the impeachment, lawmakers upheld charges against Gachagua including inciting ethnic divisions and violating his oath of office.
His several attempts to scuttle the impeachment process were dismissed by the judges but he vowed to fight his removal in court.
The 59-year-old was impeached while he was in hospital.
He argued that he was denied the right to fair hearing, adding that charges against him were not substantiated.
Gachagua, popularly known as Riggy G, is wealthy businessman from the vote-rich central Mount Kenya region, which overwhelmingly voted for Ruto in 2022 election.
He is the first deputy president to be impeached under Kenya’s revised 2010 constitution.
Kindiki, a 52-year-old former law professor who is also from the Mount Kenya region, had been a top contender to replace Gachagua.
Gachagua’s downfall is the culmination of a bitter fall-out with Ruto, which escalated after deadly demonstrations erupted in June over unpopular tax hikes, exposing divisions in the ruling party. BBC