Shareholders also backed its £2.3bn (€3.13bn) tie-up with Gala Coral.
It is a deal that Ladbrokes hopes will give it the clout to make a bigger splash online where it has been out-gunned by rivals.
The holders of 96% of Ladbrokes shares voted to approve the deal at a meeting on Tuesday.
Opposition to the merger has been led by billionaire Mr Desmond.
He claims it will not be the answer to Ladbrokes’ online problems and will instead saddle the group with debt and result in lower payouts to shareholders.
Mr Desmond, who holds a 2.8% stake, vowed after the meeting to continue the fight.
“This is only the first round of 15 rounds, or 10 rounds or seven rounds,” he said. “There’s a long way to go.”
Mr Desmond said one option would be to convene another shareholders’ meeting, for which he would need the support of the holders of 5% of the shares.
Shares in Ladbroke have had a volatile ride this year.
They have traded as high as 147p in the past 52 weeks, and yesterday were trading at 109p, slightly weaker on the day.
The bookie has a market value of £1.11bn. In Ireland, Ladbrokes local unit exited an examinership this year.
However, it cut the number of staff it employs here and the number of shops it operates.
Mr Desmond in his statement to the shareholders’ meeting said he apologised for not making his views publicly known earlier. He accused Ladbroke management of failing shareholders.
“Shareholders won’t need me to remind them of the decline in the Ladbrokes’ share price, nor the fact that peers William Hill, Betfair, and Paddy Power are 91%, 100% and 300% respectively ahead over that same [10-year] period,” he said .
“I believe there is widespread acceptance that the Ladbrokes board and management are not good enough and that performance over the last five years has been abysmal.”