DALLAS — CB Richard Ellis Group Inc., the world's largest commercial real estate broker, agreed yesterday to buy rival Trammell Crow Co. for $1.8 billion in cash to more than double its property management business.

CB Richard Ellis will pay $49.51 per share, the Los Angeles-based brokerage said in a statement. That's 27 percent more than yesterday's closing share price for Dallas-based Trammell Crow, which manages real estate in 60 countries. Including debt, the transaction is valued at about $2.2 billion.

Demand for office space is gaining worldwide even as a five-year U.S. housing boom ends. The purchase will allow CB Richard Ellis to increase its North American building management business to about 18 percent of revenue and diversify beyond leasing and sales. CB Richard Ellis now earns almost three-quarters of its revenue from commissions on renting and selling space.

"We'd like to see the revenues of our firm more evenly weighted," CB Richard Ellis Chief Executive Officer Brett White said in an interview. "The revenue associated with long-term contracts in both corporate outsourcing and institutional management are much less volatile."

Shares of CB Richard Ellis rose $1.81, or 6.4 percent, to $30.03 at 4:01 p.m. in New York Stock Exchange composite trading. Trammell Crow surged $9.65, or 25 percent, to $48.75.

International investment in commercial real-estate will gain about 26 percent to $600 billion this year as economic growth fuels demand for office space in the U.S., U.K., and other countries, according to Jones Lang LaSalle Inc., based in Chicago.

"One of the trends that you've been seeing over the last few years is institutional investors and REITs have continued to increase their ownership of commercial properties," said JPMorgan Chase & Co. analyst Michael J. Fox. "Those kind of owners are really ripe for property managers like Trammell Crow or CB Richard Ellis."