Amazon.com Inc. has reached a deal with Walt Disney Co. to carry the Disney+ streaming-video service on Fire TV devices, according to people familiar with the matter.

The two companies had been at loggerheads over terms for carrying Disney’s apps on Amazon’s Fire TV devices, the Journal reported last month. At the time, Fire TV wasn’t listed as a partner that would carry Disney’s new streaming service as a result of those disputes, The Journal reported.

Amazon...