SAN FRANCISCO — Blue Coat Systems seemed poised to begin life as a public company, after selling itself to a private equity firm last year.

Now, the cybersecurity software company plans to sell itself to Symantec instead.

Blue Coat said late on Sunday that it would sell itself to Symantec for $4.65 billion. As part of the deal, Blue Coat’s chief executive, Greg Clark, will take over as the chief executive of the combined security software maker.

To help finance the transaction, Blue Coat’s existing majority investor, Bain Capital, will invest an additional $750 million in the deal. The private equity firm Silver Lake, which invested $500 million in Symantec in February, will invest an additional $500 million.

The deal will create a big provider of security products, both the traditional antivirus kind that has long been Symantec’s focus and the newer online protection services in which Blue Coat has specialized. Executives see little overlap between the two businesses.