Disney shares rose 2.5pc to $133.57, and Verizon was up 0.3pc at $60.95 on the New York Stock Exchange at mid-afternoon. Netflix Inc shares fell 2.7pc to $270.60 on Nasdaq.
Verizon said all its new and existing unlimited wireless customers, as well as its Fios and 5G Home internet customers, will be eligible.
Disney+ launches on Nov. 12 in the United States. The service will cost $7 monthly or $70 annually. A bundle that includes ESPN+ and Hulu will cost $13 a month.
Verizon and Disney are taking a page out of Apple Inc's playbook by giving a free year's worth of the video service, to quickly build a subscriber base.
Apple plans to give away a one-year subscription to Apple TV+ for all purchasers of new Macs, iPhones and Apple TV devices. The service is set to launch on Nov. 1.
Analysts estimate Apple could sell as many as 200 million of its latest iPhones to existing users upgrading their old phones.
The Verizon deal gives Disney an advantage in the so-called streaming wars, in which companies like Netflix, Amazon.com Inc , Comcast Corp and AT&T Inc compete for streaming video subscribers.
It was not immediately clear how many Verizon subscribers would get Disney+ for free. The company does not give figures for unlimited phone plan customers.
Analysts at research firm Cowen noted that Verizon recently reduced the price of its unlimited plans by $5 per month to encourage customer uptake in preparation for 5G.
Less than half of Verizon's customers are on unlimited plans, Chief Financial Officer Matt Ellis said on the company's second-quarter earnings call.
Verizon had 124 million customers across wireless and Fios internet in the second quarter.
The move by Disney and Verizon puts added pressure on AT&T, which is announcing details of its forthcoming HBO Max streaming service at an investor day presentation on Oct. 29. AT&T has not yet released pricing or distribution details for the new service.
Last year, Verizon shut down its go90 advertising-supported streaming video service after a three-year run, after failing to reach younger viewers. It had invested millions to acquire sports and content rights from short-form video producers.