Empty Classroom from rear view.

San Francisco–based private equity firm Hellman & Friedman has agreed to buy education software company Renaissance Learning from U.K. buyout shop Permira in a $1.1 billion deal announced Thursday.

Renaissance, which is based in Wisconsin Rapids, Wis., makes cloud-based software programs that help teachers assess the reading and arithmetic skills of students in kindergarten through 12th grade. Last month, Renaissance—which also helps educators devise teaching plans based on students’ results— received a $40 million investment from Google investment fund Google Capital that valued the company at roughly $1 billion.

The Google fund is expected to stay on as a Renaissance investor following the secondary buyout, according to the announcement of the deal. The sale is expected to close in the second quarter of the year, pending regulatory approval.

Permira is unloading Renaissance less than three years after taking the company private in a roughly $500 million deal that saw founders Terrance and Judith Paul sell their majority stake.

Hellman has turned to its longtime outside counsel, Simpson Thacher & Bartlett, for legal counsel on the transaction. Simpson advised the private equity firm last November when it teamed with JMI Equity to purchase insurance software provider Applied Systems from Bain Capital for $1.8 billion. The firm also advised Hellman on its 2011 acquisition of SunGard Data Systems’ education unit in a deal valued at $1.8 billion.

The Simpson team advising on Thursday’s deal includes M&A partner Chad Skinner, credit partner Brian Steinhardt, benefits and compensation partner David Rubinsky, antitrust partner Peter Thomas, IP counsel Joshua Walker, environmental law senior counsel Michael Isby and antitrust senior counsel Michael Naughton. The Simpson associates working on the deal are Jonathan Amt, Thomas Asmar, Christian Fischer, Ellen Frye, Michelle Morad, Caroline Newton and Brian Osimiri.

Arrie Park, a former Wachtell, Lipton, Rosen & Katz attorney, serves as Hellman’s general counsel.

Skadden, Arps, Slate, Meagher & Flom, which represented Permira when it bought Renaissance, is now advising the U.K. buyout firm on the sale of the company. Skadden also advised Permira last year on its acquisition of a majority stake in Atrium Innovations in a deal that valued that company at $1.1 billion.

The Skadden team handling the Renaissance sale includes private equity partner Allison Schneirov, corporate partner Kenton King, benefits and compensation partner Regina Olshan, banking partner Stephanie Teicher and tax partner Katherine Bristor, as well as associates Barnaby Gibson and Nathan Giesselman.