In a surprise move, former New York City Mayor Rudolph Giuliani and ex-prosecutor Marc Mukasey are leaving Bracewell & Giuliani to join Greenberg Traurig. The 71-year-old Giuliani will chair the firm’s cybersecurity and crisis management practice and serve as a senior adviser to Greenberg Traurig executive chairman Richard Rosenbaum. Mukasey, 48, will co-chair the firm’s white-collar defense practice.

Giuliani, a former U.S. attorney for the Southern District of New York, joined Houston-based Bracewell in 2005, shortly before he began his unsuccessful run to be the Republican U.S. presidential nominee. To accommodate Giuliani, the firm changed its name from Bracewell & Patterson and took out a $25 million loan to open a New York office. The firm at the time also agreed to pay $10 million for the services of Giuliani Partners, a consulting firm that Giuliani still heads.

Giuliani and Mukasey say they informed Bracewell leaders of their decision on Friday. In a press release, Bracewell announced that Giuliani left under an “amicable agreement,” and that the firm will now be known simply as Bracewell. The firm’s white-collar practice is now headed by former federal prosecutor Daniel Connolly, who joined the firm with Giuliani. Bracewell’s New York office has 68 lawyers, according to the firm’s website.

In an interview on Tuesday, Giuliani said he was attracted to Greenberg’s international platform and its cybersecurity practice. The 1,900-lawyer firm has 38 offices in 10 countries, while Bracewell has roughly 450 lawyers in 10 offices.

“This has nothing to do with any disgruntlement at Bracewell,” said Giuliani. The former mayor declined to discuss his compensation package. “Of course, monetary considerations always count in decisions like this,” he said, “but the main reason [for the change] was strategic considerations.”

Giuliani declined to say if he and Mukasey had talked to other firms. “Over the last four or five years we’ve gotten a lot of different offers, but this was the first we were serious about,” he said.

Giuliani Partners will also work closely with Greenberg Traurig, especially on cybersecurity issues, which Giuliani calls “the biggest threat to America that we face as a national security matter.”

In an interview from Davos, Switzerland, Greenberg executive chairman Richard Rosenbaum said the firm had been in discussions with Giuliani for about three months. Giuliani and Mukasey are joining the firm as equity partners, he said. He declined to discuss specific compensation, but said the firm doesn’t provide guarantees, and compensation is determined by agreed levels of performance.

At the moment, no Bracewell lawyers other than Giuliani and Mukasey have joined Greenberg Traurig, but that may change, Rosenbaum said. “There is some expectation that some clients and lawyers will follow,” he said.

It’s not clear how much legal work Giuliani has been doing in recent years. In 2014 he defended video game maker Activision Blizzard Inc. in a lawsuit filed by former Panamanian dictator Manuel Noriega, who was upset over his portrayal in “Call of Duty: Black Ops II.” The suit was dismissed. He said he also helped prepare a confidential report for a large pharmaceutical company, looking at its potential exposure to regulatory risks.

Mark Evans, the managing partner of Bracewell, told sibling publication Texas Lawyer that it would remain “business as usual” in the firm’s New York office after Giuliani’s departure. He said the firm “could not have done New York” without Giuliani, but his role recently had involved more business development than client work. Evans said Giuliani has become increasingly active in cybersecurity, but that’s not something the firm does.

“We wish them well,” Evans said of the departures. He added that the firm hired branding consultants about four months ago, and on their recommendation had planned to change the name to Bracewell regardless of Giuliani’s status.

Greenberg Traurig’s Rosenbaum said Giuliani will be valuable for his broad knowledge of world affairs, as well as his legal skills. “We will be relying on Rudy’s instincts for what is going on in other sectors,” he said. He noted that Giuliani is well-known in Israel, which has become a center for cybersecurity research and development. Giuliani said that Greenberg Traurig’s office in Tel Aviv was a draw for him. “Their presence in Israel was a very big factor,” he said.

Mukasey (pictured right), the son of former U.S. Attorney General Michael Mukasey, joined Bracwell in 2005 after serving as a federal prosecutor and staff attorney with the U.S. Securities and Exchange Commission. He represented Halliburton Energy Services Inc. following the Deepwater Horizon explosion. In 2013 the company pleaded guilty to a misdemeanor charge and got three years’ probation. He also represents former Countrywide Financial executive Rebecca Mairone, who is appealing a $1 million civil fine for duping Fannie Mae and Freddie Mac into buying shoddy mortgages.

Rosenbaum said Greenberg Traurig does not have a mandatory retirement age that had to be waived for Giuliani.

“He might be 71,” he said, “but he goes very hard and is in very good shape.”