If parents of preschoolers want to plop their children in front of the laptop or tablet to watch “Blue’s Clues” and “Dora the Explorer,” they may have to join Amazon’s subscription streaming service.

On Tuesday, Viacom and Amazon announced an extensive, multiyear deal that includes granting Amazon exclusive rights to Nickelodeon’s preschool shows. The agreement — which one analyst estimated to be worth several hundred million dollars — signals that the heated battle for online streaming rights has increasingly moved to television’s youngest viewers.

In April, Netflix said it would allow its deal with Viacom to expire. Then last month Netflix struck a deal with the Walt Disney Co. to gain exclusive rights to stream Disney Jr. series like “Jake and the Never Land Pirates” and Disney XD’s “Tron: Uprising.” In 2011, Netflix introduced its “Just for Kids” menu with a selection of shows and movies aimed at children, or parents looking to entertain them. That put pressure on Amazon to secure children’s programming for its Amazon Prime subscription service, which it hopes will compete with Netflix and Hulu in the streaming video market.

In a letter to customers, Jeffrey Bezos, Amazon’s chief executive, said the deal gave Prime Instant Video more than 250 TV seasons and more than 3,900 episodes from Nick Jr., Nickelodeon, MTV and Comedy Central.