The deal will be 55 percent cash and 45 percent stock, the sources said. Both boards are expected to approve the deal, those sources told CNBC.
The deal would follow Aetna's $37 billion agreement earlier this month to acquire Humana, potentially reducing the number of major U.S. insurance companies from five to three and attracting antitrust scrutiny.
Health insurers have been in a race to consolidate, arguing that being larger would help them negotiate better prices with doctors and hospitals as well as cut administrative costs following President Barack Obama's signature healthcare law that was passed in 2010.
Anthem said in June that it had made several offers for Cigna but a deal had been delayed in part due to differences over who would lead the company and corporate governance. Cigna also said it was concerned that other members of the Blue Cross Blue Shield Association would be an obstacle.
—Reuters and CNBC's David Faber contributed to this report.