Both now own 30% each of the club with the other 40% still owned by the Icelandic investment firm CB Holdings.
They have purchased their 10% total for a fee of £8 million which has been split equally between the club and CB Holdings.
Mr Sullivan confirmed the deal on the official site, "Myself and David Gold are, like you, West Ham United fans and our aim is to ensure our club enjoys a stable and successful future. To this end, we have both invested a further £4m to increase our shareholding to 30 per cent each.
"We have a long-term intention of increasing our shareholding, while we have also invited professional investors to share in our vision for this special club. Also, in the near future we hope to extend to supporters the opportunity to invest in the club.
"We are committed to putting West Ham on a firm financial footing that will form the basis, we hope, for success both on and off the pitch."