The deal, which was concluded late on Monday night, values the club at £105million.
Mr Sullivan, a lifelong West Ham fan was brought up in Hornchurch and studied economics at Queen Mary College, Mile End.
Hammer time: David Sullivan has completed his takeover of West Ham United FC
He said: 'I have been interested in running West Ham United for 20 years and I can't wait to start work.
'I enjoyed running Birmingham City for 16-and-half years, but everyone there knew my true love was always West Ham United.
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