Yogi Adityanath, 44, has said minorities that oppose yoga should leave the country.
He once compared Bollywood actor Shah Rukh Khan to a Pakistani terrorist leader Hafiz Saeed, reports say.
Uttar Pradesh has a population of 200m people. About a fifth are Muslim.
The governing Bharatiya Janata Party won a landslide victory in the state last week with the biggest majority there since 1980. The win came after a campaign personally led by Prime Minister Narendra Modi.
Opposition MPs have criticised the appointment of Mr Adityanath, but BJP ministers defended it.
Venkaiah Naidu, minister for federal information and broadcasting, called it a “watershed moment in the history of the BJP”.
Manish Tewari, a senior Congress party leader, tweeted that the BJP’s decision to appoint Mr Adityanath was a “harbinger to greater polarisation”.
Liberals in India are asking “Why him?” but the Hindu nationalists retort by saying: “Why not?”
Uttar Pradesh has the highest number of seats in India’s lower house of parliament. So, the BJP’s recent victory there is seen as a boost for Prime Minister Modi, who will be seeking another term in 2019’s parliamentary elections.
But Mr Adityanath is widely regarded as a polarising figure because of his well-publicised anti-Muslim comments.
The BJP leaders probably believe that their election formula of consolidating the votes of the Hindu majority will help them to sail through the next general elections.
It’s a double-edged strategy: it may succeed or could galvanise the disparate opposition parties to come together. The rise of Hindu nationalists has already triggered concerns among India’s religious minorities, and the choice of Mr Adityanath is likely to intensify them.Mr Adityanath has been elected as an MP five times and is
Mr Adityanath has been elected as an MP five times and is head priest at a Hindu temple in eastern Uttar Pradesh.
He is a strong support of laws protecting cows, and opposes beef consumption.
He recently praised a travel ban ordered by US President Donald Trump to block immigration from a group of Muslim-majority countries, saying India needed something similar.