It had previously said letting people download shows added too much "complexity" to its experience.
Other video apps such as BBC iPlayer, All 4 and Amazon Prime Video already let viewers watch content when offline.
Netflix said some of its original programmes were already available to download and more would be made available in the future.
"It's surprising because just weeks ago they said it wasn't going to happen," said Tom Harrington from the consultancy Enders Analysis.
"You can understand why they wouldn't want to do it because it opens up a whole pot of rights issues. Offering a download service will cost Netflix more.
"But everyone else is already doing it. Amazon is doing it, Sky has been doing something similar with Sky Q. Netflix doesn't want to be left behind, or compared unfavourably to rivals."
Netflix is allowing some of its shows and films to be downloaded and watched offline, the company has announced.