The Valencia foundation's patrons voted for Lim's proposal, made via his company Meriton Holdings, ahead of other offers from international groups pledging significant cash injections.
"Peter Lim has completed the takeover," a Valencia spokesman told Reuters.
The next task for the new owner would be to agree a deal with lender Bankia, who are owed 220 million euros (179.1 million pounds), the spokesman added. The club's total debt is around 360 million euros.
Lim, who made a failed attempt to buy English Premier League side Liverpool in 2010, was the choice of club president Amadeo Salvo who felt the offer was the best suited to turning around the club's fortunes.
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Lim has a fortune worth $2.4 billion (1.4 billion pounds) , according to Forbes magazine, and is an avid football and sports fan.
Like many Spanish clubs, Valencia have struggled with high levels of debt and have regularly been forced to sell their top performers to stay afloat.
They failed to qualify for next season's Champions League and were knocked out of the Europa League this month by eventual winners Sevilla in the semi-finals.
With one match left, a home game against Celta Vigo later on Saturday, Valencia are 10th in the 20-team La Liga standings.
(Reporting by Tim Hanlon, editing by Pritha Sarkar)
