If the judgement, due at 10.30 a.m. local time, goes against Johnson, Parliament could be reconvened immediately, the BBC reported.
The Supreme Court will first determine whether prorogation is a matter for the courts - and, if so, whether the decision of Johnson to prorogue Parliament was lawful.
The government has said that it would "abide by the ruling" of the Supreme Court.
But Johnson, who is currently in New York for the 74th session of the UN General Assembly, has refused to rule out seeking to prorogue Parliament for a second time if the ruling goes against him.
Asked whether he would resign if the Supreme Court ruled against him, Johnson told the BBC: "I'm going to wait and see what the judgement is," adding that the government "fully respects the law and fully respects the judiciary".
Parliament is currently due to return on October 14, with the UK scheduled to leave the European Union (EU) on October 31.
The three-day hearing at the Supreme Court dealt with two appeals - one from campaigner and businesswoman Gina Miller, the second from the government.
Miller was appealing against the English High Court's decision that the prorogation was "purely political" and not a matter for the courts, while the government was appealing against the ruling by Scotland's Court of Session that the prorogation was "unlawful" and had been used to "stymie" Parliament.
The challenge in the Scottish Court was brought by a cross-party group of MPs and peers led by the Scottish National Party's (SNP) Joanna Cherry.
( With inputs from IANS )