Kayak Software Corp., the New England company known for its quirky ­office culture and colorful executives as well as its speedy travel searches, will be acquired by Priceline.com Inc. for $1.8 billion in cash and stock, the companies said Thursday.

The merger, if approved by shareholders, would join two of the best-known brands for booking hotels, rental cars, and airline tickets over the ­Internet. The deal would help Priceline build its US market, analysts said, while gaining access to Kayak’s Internet and mobile technology — and its stable of technologists.