Exhibit 99.1

Aspen Insurance Holdings Announces $150 million Accelerated Share

Repurchase Program

Hamilton, Bermuda, February 26, 2013 – Aspen Insurance Holdings Limited (“Aspen” or “the Company”) (NYSE: AHL) today announces that it has entered into an Accelerated Share Repurchase (“ASR”) agreement with Goldman, Sachs & Co. (“Goldman”) to repurchase an aggregate of $150 million of Aspen’s ordinary shares under an accelerated share repurchase program. From January 1 through February 26, 2013, Aspen also repurchased approximately $47 million of its ordinary shares in the open market.

Under the ASR agreement, Aspen will pay $150 million to Goldman in exchange for Aspen’s ordinary shares. Aspen expects the substantial majority of shares to be delivered on March 1, 2013. The total number of shares ultimately repurchased under the agreement will be determined based on a discount to the average daily volume-weighted average price of Aspen’s ordinary shares during the ASR period. At settlement, Goldman may be obligated to deliver additional shares to Aspen, or Aspen may be obligated to make a delivery of shares or a payment of cash to Goldman, at Aspen’s election. Aspen anticipates that all repurchases under the ASR will be completed no later than October 3, 2013.

Based on Aspen’s closing share price on February 26, 2013, the ASR program and the completed open market share repurchases from January 1, 2013 together represent approximately 8 per cent of the Company’s current total market capitalization. Aspen will have approximately $335 million remaining under its current $500 million share repurchase program authorized by the Board of Directors and announced on February 7, 2013. The ordinary shares will be retired once repurchased.

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About Aspen Insurance Holdings Limited

Aspen provides reinsurance and insurance coverage to clients in various domestic and global markets through wholly-owned subsidiaries and offices in Bermuda, France, Germany, Ireland, Singapore, Switzerland, the United Kingdom and the United States. For the year ended December 31, 2012, Aspen reported $10.3 billion in total assets, $4.8 billion in gross reserves, $3.5 billion in shareholders’ equity, and $2.6 billion in gross written premiums. Its operating subsidiaries have been assigned a rating of “A” (“Strong”) by Standard & Poor’s, an “A” (“Excellent”) by A.M. Best and an “A2” (“Good”) by Moody’s Investors Service.

Application of the Safe Harbor of the Private Securities Litigation Reform Act of 1995

This press release contains “forward-looking” statements regarding future results and events, including, without limitation, statements regarding the Company’s intention to repurchase its ordinary shares from time to time under the Company’s share repurchase program, the timing and amounts of repurchases, the intended use of any repurchased shares and the source of funding for the share repurchase program. Forward-looking statements include all statements that do not relate solely to historical or current facts, and can be identified by the use of words such as “expect,” “intend,” “plan,” “believe,” “project,” “anticipate,” “seek,” “will,” “estimate,” “may,” “continue,” and similar expressions of a future or forward-looking nature.

All forward-looking statements rely on a number of assumptions, estimates and data concerning future results and events and are subject to a number of uncertainties and other factors, many of which are outside Aspen’s control that could cause actual results to differ materially from such statements, including our ability to consummate the transactions contemplated by the terms of the accelerated share repurchase agreement, the share price and share volumes which may impact timing of repurchases, changes in market conditions and the impact on our business of such factors. For a detailed description of uncertainties and other factors that could impact the forward-looking statements in this press release, please see the “Risk Factors” section in Aspen’s Annual Report on Form 10-K for the year ended December 31, 2012, filed with the U.S. Securities and Exchange Commission on February 26, 2013. Aspen undertakes no obligation to update or revise publicly any forward-looking statements, whether as a result of new information, future events or otherwise.

For further information

Please visit www.aspen.co or contact:

Investors

Kerry Calaiaro, Senior Vice President, Investor Relations, Aspen

Kerry.Calaiaro@aspen.co

+1 646 502 1076

Media

Steve Colton, Head of Communications, Aspen

Steve.Colton@aspen.co

+44 20 7184 8337

International – Citigate Dewe Rogerson

Caroline Merrell or Jos Bieneman

caroline.merrell@citigatedr.co.uk

jos.bieneman@citigatedr.co.uk

+44 20 7638 9571

North America – Abernathy MacGregor

Allyson Vento

amv@abmac.com

+1 212 371 5999

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