Rovi Corp. has agreed to acquire set-top box company TiVo Inc. for about $1.1 billion, a tie-up that comes as Americans’ viewing habits are evolving quickly.

Rovi, which provides technology for electronic TV guides, DVRs and video-on-demand services, said on Friday it would pay $10.70 a share in cash and stock for TiVo. That is a premium of about 40% over TiVo’s closing price of $7.66 on March 23, the last trading day before media reports about talks on a deal.

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