EA made the bid earlier this month, offering shareholders $26 per share. Take-Two's board of directors and a panel of advisors took nine days to unanimously reject the offer.
The deal would have given EA control over all of Take-Two's properties, including Rockstar Games, developer of the controversial Grand Theft Auto franchise. The fourth GTA game is due on 29 April.
Take-Two did not entirely rule out making another deal with EA, however, or agreeing to a different acquisition offer.
The company said that it would look at alternatives which "may include a business combination with third parties or with EA, remaining independent, or other strategic or financial alternatives".