Special Judge Arun Bhardwaj allowed Kochhar's plea while asking him to furnish a personal bond of Rs 25 lakh and a surety of the like amount.
Kochhar told the court that he wanted to visit his son and grandchildren in Singapore between June 12 and 20, and thereafter wanted to travel to the UK from July 4 to 23.
Allowing his plea, the court directed him to inform it about his arrival in India from Singapore and to surrender his passport before the court within 48 hours of his return from UK.
The court also asked him to provide his address where he would be staying in Singapore and UK and the mobile number on which he would be available during his visits.
The court directed him not to request for extension of his stay abroad.
The court also directed him not to tamper with the evidence or influence witnesses in any manner and to not use the permission granted to him contrary to the rules.
The Central Bureau of Investigation (CBI) have opposed Kochhar's plea seeking permission to visit Singapore and the UK.
The CBI had in April 2018 filed a charge sheet against former Railway Minister Lalu Prasad, his wife Rabri Devi and son Tejashwi Yadav for the alleged irregularities in the allotment of contracts of two IRCTC hotels in Ranchi and Puri in 2006 to a private firm.
According to the charge sheet, the contracts were given to Sujata Hotels, a company owned by Vijay and Vinay Kochhar, in lieu of a bribe in the form of a three-acre commercial plot at a prime location in Bihar's Patna district.
( With inputs from IANS )