Quest Software Inc. shareholders have approved Dell Inc.’s pending $2.4 billion takeover, the Aliso Viejo-based company announced Tuesday.

The deal had already gained approval from both of the company’s boards, and is now subject to customary closing conditions.

Round Rock, Texas-based Dell, the world’s third-largest computer maker, won a four-month bidding war to acquire Quest. It has said plans to use the company as the foundation to grow software sales past the $5 billion mark in the coming years as it diversifies its product offerings beyond computers.

Quest makes software that helps manage and improve other business products from various companies, including Washington-based Microsoft Corp., IBM Corp. of New York, and Redwood Shores-based Oracle Corp.

All of those companies had been considered prospective suitors for Quest amid a budding bidding war.

Quest is one of Orange County’s biggest software makers, with $857 million sales in 2011. It has 3,000 workers overall, with about 600 here.

Quest shares hit a 52-week high of $28 during today’s trading session, boosting its market value to about $2.37 billion.

Dell’s shares were down nearly 2% at the end of trading Tuesday with a market value of about $17.31 billion.