Tyagi, who retired in 2007, was questioned by the CBI extensively in the past in this case.
Along with Tyagi, his cousin Sanjiv alias Julie Tyagi and lawyer Gautam Khaitan were also arrested.
"This is for first time a former IAF chief has been arrested by the central probe agency," official sources said.
On January 1, 2014, India had scrapped the contract with Finmeccanica's British subsidiary AgustaWestland for supplying 12 AW-101 VVIP choppers to the IAF over alleged breach of contractual obligations and charges of paying kickbacks of Rs 423 crore by it for securing the deal.
CBI had also got issued Letters Rogatory (judicial requests) to multiple countries to gather more leads and evidences in this case.