Central Bureau of Investigation (CBI) Special Judge Arvind Kumar allowed Tyagi's bail application and asked him to furnish a personal bond of Rs 2 lakh and a surety of like amount.
Tyagi and two others, arrested on December 9, were sent to the judicial custody till December 30.
Tyagi -- the first chief of any wing of the armed forces to be arrested in the country -- and the others were allegedly involved in irregularities in the procurement of 12 AW-101 VVIP helicopters from Britain-based AgustaWestland.
Tyagi has denied the charge.
The other two accused in the case have also sought the bail from the court.