The SC order came on Yachury's habeas corpus petition challenging the detention of Tarigami ahead of the abrogation of Article 370 by the government on August 5. The plea also stated that Tarigami was not in good health and Yechury wanted to meet him.
Solicitor General Tushar Mehta opposed Yechuri's plea saying his visit to the state could be used for political purposes.
However, Yechury's counsel senior advocate Raju Ramachandran said the CPI-M leader was ready to give an undertaking that he was only going to meet his colleague.
The court instructed Yechury to not use his visit for any other purpose and told Mehta that the government was free to stop the CPI-M leader and send him back if he did anything in violation of the court order.
"If a citizen wants to go any part of the country, he must be given access," said the bench headed by Chief Justice Ranjan Gogoi.
The court also rejected Mehta's offer of giving Yechury an escort during his visit. "There is no need of providing security," it said.
Yechury had earlier tried to visit Kashmir with CPI General Secretary D. Raja on August 9. But the two leaders were detained at the Srinagar airport and sent back home.
On August 24 again, he accompanied an Opposition delegation, including former Congress president Rahul Gandhi, to Srinagar. But the group was detained and prevented from getting outside the airport.
In another habeas corpus plea filed by law graduate Mohammad Aleem Syed seeking information on the whereabouts of his family in Kashmir, the top court allowed Syed to travel to Anantnag and meet his parents.
The court also ordered the Jammu and Kashmir administration to facilitate Syed's travel and provide him police protection. It directed him to file a report after meeting his parents.
( With inputs from IANS )