Dell Inc. and Silver Lake Management LLC have secured the votes needed for approval of their proposed $24.9 billion leveraged buyout, according to a person with knowledge of the matter.

Holders of two-thirds of the voting shares have indicated their support for the proposed transaction, the largest leveraged buyout since 2007, said the person, who asked not to be identified because the outcome isn’t public.

Michael Dell is finally poised to have his buyout sewn up after a seven-month contest that left the fate of the world’s third-largest computer maker in doubt for much of the year. Billionaire financier Carl Icahn dropped his opposition to the deal yesterday, removing what for several months was one of the largest obstacles to getting the buyout approved.

“It’s going to make the shareholder meeting a lot easier,” Shannon Cross, an analyst at Cross Research, said of Icahn’s decision.

The results of the voting will be disclosed at a Sept. 12 meeting at Dell’s Round Rock, Texas, headquarters. Three previous shareholder events were adjourned as CEO Dell and Silver Lake lacked the votes they needed to secure approval. David Frink, a spokesman for Dell, declined to comment.

Investors, including Franklin Mutual Advisers and BlackRock Inc., are supporting the offer after the buyout group sweetened its proposal to $13.75 a share, plus a 13-cent special dividend and guaranteed payment of the company’s third-quarter dividend.

“While we of course are saddened at our losing the battle to control Dell, it certainly makes the loss a lot more tolerable in that as a result of our involvement, Michael Dell/Silver Lake increased what they said was their ‘best and final offer,’” Icahn wrote in a letter yesterday. “As a result of this increase all stockholders are to receive many hundreds of millions of dollars more than the board originally accepted.”