A Special Cell team arrested Jani under Section 41(1) of CrPC and will hand him over to the New Delhi district police, a senior official said.
Jani had earlier claimed on social media that he would surrender but apparently kept changing his mind.
On April 15, a loaded gun and a letter purportedly signed by Jani, threatening to behead Kanhaiya and Khalid, were found in a bus plying between Kashmere Gate and Vasant Vihar via JNU campus.
The driver of the bus took the vehicle to Tilak Marg Police Station and reported the matter, following which a case was registered.
Two days later, police arrested Jani's brother Saurabh and his friend Sulabh here in connection with the incident. Later, another man was arrested but Jani had remained at large.
The police had unsuccessfully raided his office in Lajpat Nagar area and several possible hideouts in Delhi-NCR.
Jani had earlier threatened Kanhaiya over a Facebook post claiming that his men, at least 10 of whom are armed, are present inside JNU campus and can attack him anytime.
Celebrating azaadi: Listening for the concern behind the complaint
Umar, Anirban challenge rustication: HC seeks JNU reply
Umar Khalid taken to AIIMS, withdraws hunger strike
Kanhaiya discharged from AIIMS, ends hunger strike
JNU's Umar Khalid granted permission to visit Kolkata