Dipak Bharti, a Class IX student of the local DAV school, who was kidnapped on January 25, was released on Wednesday.
Dipak's release follows that of Kislay Komal, a Delhi Public School student in Patna earlier in the day.
Police claimed that Dipak was released under police pressure.
Deputy Inspector General of Police, Bhagalpur, Kumar Rajesh Chandra said that the police had arrested a criminal Jay Govind Verma, who had made ransom call to the boy's family. On the basis of clues provided by the man, the police conducted intensive raids in Kankaithi village under Jagdishpur police station of Bhagalpur district.
The kidnappers, frightened by the police action, released Dipak, he said.
More details about the boy's return are awaited.
The kidnapping, which took place after that of Kislay, had triggered widespread agitation in Bhagalpur with students taking out protest marches in the town and sending a memorandum to President APJ Abdul Kalam appealing for Dipak's release.
A bandh had also been observed in the town on January 28.