Special CBI Judge Arvind Kumar gave the relief to both the accused on a personal bond of Rs 2 lakh each and one surety of like amount while imposing certain conditions on them.
The court ordered them not to tamper with the evidence or try to influence the witnesses.
The court had earlier granted bail to 72-year-old former IAF chief Tyagi, saying that CBI has failed to state the alleged bribe amount and when it was paid.
Tyagi, who retired in 2007, his cousin Sanjeev and Khaitan were arrested on December 9, 2016 by CBI in connection with the case which relates to procurement of 12 VVIP choppers from UK-based firm during the UPA-2 regime.
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Sanjeev's counsel had also opposed CBI's contention saying there was no reason to claim that if granted the relief, his client would hamper the probe.
The accused sought bail on the grounds that the evidence was documentary in nature and had already been seized by CBI and they have cooperated with the probe agency.
Sanjeev and Khaitan were lodged in judicial custody.
The ED had pressed for an open-ended NBW to bring James
from the UK to face trial. An open-ended NBW does not carry a time limit for execution.
In June last year, the ED had filed a 1,300-page prosecution complaint (equivalent of a charge sheet) in connection with its money laundering probe in the case.
It had claimed that its probe had found that James had allegedly received Euro 30 million (about Rs 225 crore) from M/s AgustaWestland and alleged that this was nothing but kickbacks paid by the company to execute the deal for sale of 12 helicopters to India in favour of the firm in the guise of genuine transactions for performing multiple work contracts.
The complaint delved into the detailed role of James in the deal, his multiple visits to India and his transactions.
The first complaint in the case was filed in November 2014.
According to sources, the ED has already sought extradition of James from the UK.
In its complaint, the ED also claimed that the three middlemen "managed" to make inroads into the Indian Air Force in order to influence and subvert the force's stand regarding reducing the service ceiling -- the altitude at which a helicopter can fly -- from 6,000 to 4,500 metres in 2005 after which AgustaWestland became eligible to supply the dozen choppers for VVIP flying duties.