Special CBI Judge Arvind Kumar granted the relief to Tyagi on a personal bond of Rs two lakh and one surety of like amount.
A Delhi court hearing the matter directed the former air chief not to leave Delhi-NCR and not to tamper with evidence.
The court will hear the bail plea of the other two accused- Sanjeev Tyagi and Gautam Khaitan on January 4.
The Central Bureau of Investigation (CBI) counsel earlier on December 23 requested the court not to disclose evidences to anyone saying that if the evidence gathered will be disclose, there would be implication on future investigation.
The Patiala House court had on December 17 remanded the trio to judicial custody till December 30 as their CBI custody ended.
Earlier, the CBI had moved the court seeking a 10-day custody to interrogate Tyagi and the other accused in the case.
Tyagi has been accused of influencing the deal in favour of Agusta Westland during his tenure as the IAF chief.
He has, however, repeatedly denied the allegations.
During the hearing of the bail plea, S P Tyagi's advocate Maneka Guruswamy had said that her client "could not be deprived of freedom if the investigation is taking time to complete".
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.
Additional Solicitor General Tushar Mehta, appearing for CBI, had opposed the bail pleas of the accused, saying if set free, they might influence witnesses and hamper the "multi-layered probe by various agencies in more than one jurisdictions involving several countries".
"We have evidence where the meetings unofficially took place for the purpose of crime. At this stage, please do not entertain their bail pleas. Let the probe be completed," he said, seeking dismissal of the bail pleas of all the three accused and adding that the matter has "tarnished country's name".
On the court's query whether the CBI had any material regarding S P Tyagi receiving money, the agency told the court that the former IAF chief had purchased several properties for which the sources of income were not disclosed by him and alleged that he had abused his official position.