Online travel agency will buy travel metasearch company Kayak for $1.8 billion.

Priceline will pay $40 a share for Kayak, including $1.3 billion in stock and $500 million in cash, the companies said Thursday afternoon.

The purchase price represents a 29% premium over Kayak’s closing price Thursday.

Kayak, founded in 2004, went public at $26 a share last July, 20 months after first filing for its initial public offering.

Kayak said Thursday that its third-quarter net income rose 14% from a year earlier to $8 million, while revenue jumped 29% from a year earlier to $78.6 million.

Year to date, Kayak’s net income jumped fivefold from a year earlier to $19.4 million. Revenue was up 34% to $228.9 million.

Priceline in 2010 overtook Expedia to become the world’s largest online travel agency by sales, though Expedia has about four times Priceline’s share among U.S. travelers.

Follow Danny King on Twitter @dktravelweekly.

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