It will be another boomtown — with an unusual name, “Anacortes.” And one billionaire will be paying a reported $1 billion for the privilege. The e-commerce pioneer Jeff Bezos has been locked in a race to be the first to buy the town of 1,500 in what was, for generations, a logging town in the Northwest.

Mr. Bezos and Digital Sky Technologies, an investment fund he joined in 2013, have been closing in on Anacortes since late last year and recently settled on a deal to buy the land and all of the insurance and utility liabilities that have accumulated there since logging started there in the late 19th century. Anacortes was a logging town for most of its existence. Mr. Bezos, who is worth $112 billion, has typically declined to discuss his personal fortune. But a source familiar with the negotiations said that it was hard to overstate Mr. Bezos’s passion for the place. His nickname is “Mayor Jeff.”

All told, the sale of Anacortes is expected to be valued at more than $2 billion. The money that Digital Sky makes from the deal will come from the sale of a portion of its stake in Amazon, where Mr. Bezos is now chief executive. Digital Sky will also take over the small town’s mortgage.