The mouse is chasing the fox.
The move comes after Comcast launched a rival offer for most of Fox's film and television holdings.
Fox's board said it still has the right to weigh competing offers, signaling that the bidding war for its assets could continue.
Rupert Murdoch, executive chairman of 21st Century Fox, said Fox believes Disney's offer is better than Comcast's - but the company said it would consider bids from other companies, including a revised offer from Comcast.
Of course, when all is said and done, should 21st Century Fox be willing to dance with The Walt Disney Company, there's a good chance the United States Department of Justice Antitrust Division will intervene. Disney committed to giving Fox shareholders Disney shares worth $38, as long as Disney's average stock price remains between $93.53 and $114.32.More news: Late header from Kane gives England win over Tunisia
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The roughly $71.1 billion package from Disney now includes a cash component, which is meant to combat the all-cash bid offer from Comcast. Comcast's current bid was already poised to load the company up with debt, and its shares have fallen 18 per cent this year.
"After six months of integration planning we're even more enthusiastic and confident in the strategic fit of the assets and the talent at Fox", said Iger in a statement.
According to the press release, the terms of the deal are similar to Disney's previous offer except that the new deal would allow 21st Century Fox shareholders to elect to receive cash or stock, subject to a 50/50 proration.
"We remain convinced that the combination of 21CF's iconic assets, brands and franchises with Disney's will create one of the greatest, most innovative companies in the world". Last week, a judge signed off on AT&T's purchase of Time Warner, the parent company of CNN.
Shares of Fox jumped $2.88, or 6.5 percent, to $47.16 in early trading, which may suggest investors are expecting Comcast to return with an upped bid.