The parliament confirmed Sheikh Sabah as the new emir on Sunday following last week's ousting of Sheikh Saad al-Abdullah al-Sabah for health reasons.
"Today, we turn a new page of the history of Kuwait... We look forward to a promising future," Sheikh Sabah told MPs.
"Kuwait witnessed a unique experiment over the past few days... marred with some pain and anxiety. But in the end, democracy and the constitution prevailed," Sheikh Sabah said.
He called for national unity in the face of regional challenges and pledged to continue with reforms.
The fifty members of the parliament, in addition to the 14 members of the cabinet - excluding the PM himself - unanimously voted for Sheikh Sabah as the country's new ruler.
"I swear to respect the constitution and the state laws, and to protect the people's freedoms ... the independence of the homeland and the integrity of its territory," he said as he took oath in front of the emirate's legislators.
Ousted Sheikh Saad, who was the country's crown prince, had automatically become the emir of Kuwait after the death of his predecessor and cousin Sheikh Jaber al-Ahmad al-Sabah on January 15.
The Gulf state became embroiled in its most serious domestic political crisis until the elected parliament deposed Sheikh Saad in an unprecedented vote that made Sheikh Sabah the undisputed leader of the country.
During a 10-day crisis Sheikh Sabah was given a clear mandate by the al-Sabah ruling family, the elected parliament, the local press and the business community.
Sunday’s unanimous vote came amid parliamentary calls to appoint a new crown prince and a prime minister, and to speed up reforms.
The appointment of a new prime minister is the most immediate task for Sheikh Sabah as he has a year before he must appoint a new crown prince.
The posts were split in 2003 when Sheikh Sabah was himself appointed premier due to the ill-health of Sheikh Saad, who was then crown prince and prime minister.
Liberal MP Ali al-Rashid called upon Sheikh Sabah to "continue separating the posts of the crown prince and the prime minister."
The constitution gives the emir the sole authority of appointing both his heir apparent and the prime minister. He also has the final word on the selection of cabinet ministers.