Once confirmed, he is expected to endorse a new, military-drafted constitution and to start appointing his own team of senior royal officials.
His father, King Bhumibol Adulyadej, the world's longest-reigning monarch, died on 13 October, aged 88.
The government has declared a year-long official mourning period.
The widely revered king had served 70 years as head of state, and was seen as a stabilising figure, promoting economic development and social harmony in a country hit by cycles of political turmoil and multiple coups.
The BBC's Jonathan Head in Bangkok says there have been concerns expressed quietly over how well his son will perform the same role.
Following King Bhumibol's death, he had delayed taking the crown in order to join the people in mourning.
The crown prince, who is 64, is much less well known to Thais than his father, and does not have his widespread popularity.
Our correspondent says the crown prince will start his reign under a military government that is likely to dictate Thailand's political arrangements for several more years.
He is also likely to start appointing his own advisers to senior positions in the palace hierarchy, ending the influence of a number of elderly but powerful men who had served King Bhumibol.
Strict lese-majeste laws protect the most senior members of Thailand's royal family from insult or threat. Public discussion of the succession can be punishable by lengthy jail terms.
Prime Minister Prayuth Chan-ocha also said on Tuesday that restrictions on entertainment and television in place since the king's death would be lifted on 14 November.
He said: "In terms of entertainment - soap operas and movies - they can go ahead. We simply ask for co-operation. Some programmes need to lower their tone."
TV channels stopped normal broadcasting moments after the death was confirmed, and switched to broadcasts from the Grand Palace and archive footage of the royal family.
The PM said that people should still maintain decorum throughout the mourning period and refrain from wearing "inappropriate attire".
Crown Prince Maha Vajiralongkorn is to be confirmed as the new king of Thailand on 1 December, a senior source has told the BBC.