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The appointment of Schwimmer, an American who has been with Goldman for 20 years and most recently served as global head of market structure and global head of metals and mining in investment banking, takes effect on Aug. 1.
Frenchman Rolet stepped down last year after almost a decade at the helm, during which he transformed the company with a string of deals, lifting its market value to almost 14 billion pounds ($19.9 billion) from less than 1 billion.
Schwimmer takes charge as Britain's planned departure from the European Union in 2019 raises questions about the LSE's strategy at the heart of Europe's biggest financial centre.
Schwimmer will have to protect LSE's dominance in clearing, as it risks losing a chunk of its derivatives clearing business to Deutsche Boerse because of Brexit.
"David is a leader with great experience in the financial market infrastructure sector ... as well as capital markets experience in both developed and emerging markets," LSE Chairman Donald Brydon said in a statement.
Schwimmer's appointment should also help allay investor concerns that LSE could be more vulnerable to a potential takeover without a permanent chief executive.
Schwimmer, 49, who attended Harvard Law School and Yale University, would have an annual salary of 775,000 pounds, with a bonus of up to 225 percent of his salary, LSE said.
"He (Schwimmer) is well known for his robust intellect and partnership approach with clients and colleagues alike," Brydon said on Friday.
LSE said group CFO David Warren, who was acting CEO, would continue as the company's finance boss.
Activist hedge fund TCI, an LSE investor, predicted a 15 billion pound bid for the group from transatlantic rivals ICE and CME Group during an investor conference call earlier this year.
Rolet's exit triggered a fight between Brydon and TCI, whose attempt to push him out was eventually defeated at a shareholder meeting.
The British firm holds a 5.18 percent stake in LSE.
Rolet was credited with turning LSE into a diversified exchange group by buying a controlling stake in LCH, one of the world's biggest clearing houses, and expanding the bourse's activities in stock indexes.
Under Rolet's leadership, LSE was unable to seal a merger with Deutsche Boerse, the exchange's third attempt at an Anglo-German tie up.
"It hasn't been an orthodox transition, but we're pleased to see clear leadership being put in place," said a top-20 investor in LSE.
LSE's shares were up 0.7 percent at 4269 pence at 0900 GMT
($1 = 0.7006 pounds)
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)