Special CBI Judge Arvind Kumar granted the relief to Tyagi on a personal bond of Rs two lakh and one surety of like amount.
The court, however, imposed certain conditions on the accused and asked him not to try to influence the witnesses and hamper the probe.
The bail applications of other two accused - Tyagi's cousin Sanjeev Tyagi and lawyer Gautam Khaitan - are pending before the court which said it will decide both the pleas on January 4.
She had claimed before the court that in the last four years since the FIR was registered, the CBI has never been able to confront Tyagi with any incriminating evidence till date.
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Advocate Pramod Kumar Dubey, counsel for Khaitan, had
also countered CBI's argument, claiming that the agency was trying to sensationalise the matter and there was no allegation that his client had not joined the probe or tried to influence it.
Sanjeev Tyagi's counsel Manav Gupta also opposed CBI's contention saying there was no reason to claim that if granted the relief, his client would hamper the probe.
The court had on December 17 sent all the three accused to judicial custody till December 30.
71-year old Tyagi, who had retired in 2007, his cousin Sanjeev and Khaitan were arrested on December 9 by the agency in connection with the case. The case relates to procurement of 12 VVIP choppers from UK-based firm during the UPA-2 regime.
The accused have alleged that the "CBI was trying to extract the confession using force". The defence counsel had also claimed that there was no apprehension of them fleeing from justice or tampering with evidence.
It had submitted that "one part of the crime was committed in India while various other angles are in foreign land."
Tyagi's counsel had earlier claimed that the decision to procure VVIP choppers from AgustaWestland was a "collective" one and Prime Minister's Office (PMO) was also a part of it.