The country has been plunged into mourning since widely revered King Bhumibol Adulyadej died on 13 October, ending a remarkable seven-decade long reign and removing a key pillar of unity in a bitterly divided nation.
Today's cabinet announcement puts to bed anxiety over succession that was sparked when the junta made a surprise announcement after Bhumibol's death that the prince had asked to delay his official proclamation so he could mourn.
"The prime minister's secretary will notify the National Legislative Assembly," he told reporters after a special cabinet meeting.
According to procedure, the assembly speaker then has to formally invite the Crown Prince to become monarch before proclaiming the new king to the public.
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Prawit said the Thai parliament's president would likely receive a royal audience "either tomorrow or the day after".
Proclamation is expected shortly after the audience.
Vajiralongkorn, 64, has been the named successor to King Bhumibol Adulyadej for more than four decades.
A military source told AFP the prince was still currently in Germany.
He will soon inherit one of the world's richest monarchies, an institution protected by a harsh royal defamation law.
That law makes open discussion about the royal family's role all but impossible inside the kingdom.
Officially Thailand's monarch has limited constitutional power.
But over his seven-decade reign, Bhumibol built up a powerful network of alliances, especially within Thailand's powerful military elite, and forged a reputation as an arbiter in times of crisis.
Thailand's last decade has seen a cycle of political protests, coups by an arch-royalist military while inequality has deepened.
The latest coup was in 2014.