"It is the view of the Sophos board that this is a compelling offer for Sophos shareholders which secures the delivery of future value for shareholders today," added Sophos Chairman Peter Gyenes.
The deal must still be approved by shareholders.
"Thoma Bravo has deep sector expertise in cybersecurity software as well as a long and successful track record of partnering with and investing in its portfolio companies to support long-term growth and success," said Gyenes.
"Under Thoma Bravo's ownership we expect Sophos to accelerate its evolution and leadership in next-generation cybersecurity."