Peter Morgan/Associated Press

Verizon Communications on Thursday announced it would buy I.T. services provider Terremark Worldwide for $19 a share, in a deal valued at $1.4 billion.

The offer represents a 35 percent premium to Terremark’s closing price on Thursday. The board of Terremark unanimously approved the deal.

The deal for Verizon is a play on the rapid growth in remote, or cloud computing, an area where the company has been lagging behind competitors like AT&T. Terremark, provides data storage services for big companies and government agencies.

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“For Verizon, $1.4 billion is a drop in the bucket and it provides a lot of strategic value,” said Colby Synesael, an analyst at Cowen And Company.

Verizon knows Terremark’s work firsthand. Last year, Verizon signed a deal for 25,000 square feet in Terremark’s data centers. The company also started selling Terremark’s hosting services.

“Cloud computing continues to fundamentally alter the way enterprises procure, deploy and manage IT resources, and this combination helps create a tipping point for ‘everything-as-a-service,'” Lowell McAdam, president and chief operating officer of Verizon, said in a statement. “Our collective vision will foster innovation, enhance business processes and dynamically deliver business intelligence and collaboration services to anyone, anywhere and on any device.”

Revenue at Terremark increased 22 percent to $84.9 million in the latest quarter — although the company posted a loss of 12 cents a share.

Cloud computing has been a hot area for deal-making. In recent months several technology giants, including Hewlett-Packard, EMC, Dell and I.B.M., have bought a slew of data storage companies. In mid-December, Dell announced plans to buy Compellent Technologies, an acquisition that valued the company at nearly $1 billion.

After Terremark, Mr. Synesael figures more deals could follow. Among the potential targets: Savvis, Rackspace Hosting, Internap Network Service and NaviSite.

Verizon was represented by Goldman Sachs and Weil, Gotshal & Manges in the deal, while Terremark worked with Credit Suisse Securities and Greenberg Traurig.