Icelandic bank Straumur said it had sold subsidiary CB Holding's 50 percent stake and Sullivan and Gold would take immediate operational and commercial control.
Straumur, who said the deal valued the strugglers at 105 million pounds, retained the other 50 percent although Sullivan expected to attract more investment.
Sullivan and Gold backed team manager Gianfranco Zola and said the key to restoring West Ham's place as a force in English football would be to move into the nearby 2012 Olympic Stadium.
"I would say if it's not 50-50 (we will take over the stadium) I would be very surprised," Sullivan told reporters.
He added that spending around 50 million pounds to buy half the club made "no financial sense" and he and Gold had only done it to save the club they support. He said they could not afford a complete buyout at present.
Outlining the perilous position of the club's finances, Sullivan said the total debts were 110 million pounds.
"There's 50 million owed to banks, 40 million owed to other clubs. There's not a penny to come in, they (previous owners) have borrowed against the next two years of season-ticket money," he said.
"Sponsors have paid 70 percent of their three-year (deals) up front. We wouldn't buy this club at all if this wasn't West Ham. It makes no commercial sense for anyone to buy this club and it's amazing two other people wanted to buy it."
One of the other bidders was Tony Fernandes, chief executive and founder of AirAsia, who until Monday night was considered favourite to buy the club.
"Deal lost on West Ham. Hopefully new owners protect what's good. We gave awesome deal and new ideas to rejuvenate a club," Fernandes posted on his Twitter social networking site.
With West Ham floundering in 16th place in the table and only out of the relegation zone on goal difference, the immediate priority is to make sure the club stay in the top flight.
TRANSFER WINDOW
While a sudden influx of new signings is unlikely, it appears West Ham will be able to keep their leading players during this month's transfer window.
"The position was if somebody didn't buy the club in the next 10 days they would have had to raise eight million in the transfer window to survive," Sullivan said.
West Ham-born Gold, who with Sullivan helped transform the fortunes of Birmingham during 16 years there before selling the club to Hong Kong businessman Carson Yeung in October, said a meeting was planned later on Tuesday with Zola to discuss how to strengthen the team.
"We will sit down with Franco tonight and see what he has to say," Gold said. "He will guide us and tell us of his requirements. We will do everything we can to help him.
"The driving force is to make absolutely sure we have done everything possible to make sure West Ham stay up."
Finances plunged into the red after the club spent millions in 2007 to avoid relegation under former chairman Eggert Magnusson and the situation
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