The Valencia Foundation's patrons voted for Lim's proposal ahead of other offers from international consortiums offering large cash injections.
"Peter Lim has completed the takeover," a club spokesman told Reuters.
The spokesman added that the next task for the new owner will be to agree a deal with creditors Bankia, who are owed 220 million euros (9.78 billion baht). The club's total debt is around 360 million euros.
Lim was the choice of club president Amadeo Salvador who felt that his offer was best suited to turning around the fortunes of the club which failed to qualify for next season's Champions League and were knocked out of the Europa League earlier this month by eventual winners Sevilla in the semi-finals.
Valencia are 10th in the 20-team La Liga standings.