The network will air seasons two to four featuring from May 9, Deadline reports.
After Tennant's first episode as the Doctor is shown on May 9, the series will continue on June 13 with eight episodes until June 20.
"Disney XD is recognised for its family-friendly programming, making the channel a great partner to introduce the David Tennant seasons of Doctor Who to a new generation of viewers," BBC Worldwide's North America EVP Matt Forde said.
Disney XD's general manager Marc Buhaj added: "This iconic series features the high-quality, high-stakes action and adventure storytelling that our viewers love.
"The show headlines one of the most charismatic lead characters in television in the form of the Doctor and showcases a compelling rogues' gallery of villains from around the universe."
Pay TV subscribers will also be able to catch episodes on demand through the Watch Disney XD app from June 14.
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