Bechtel, one of the largest engineering, construction and project management companies in the world, will relocate several hundred jobs from Frederick County to Fairfax County.

In moving what it calls its global operations headquarters to the Reston Town Center, Bechtel will bring 625 jobs and an $18 million investment to Fairfax and give Virginia the latest round of bragging rights in the commonwealth’s cross-border rivalry with Maryland to land big businesses.

Maryland, which recently agreed to pay Bechtel nearly $10 million to ensure that the company’s 1,250 other employees in Frederick remain there, said the company’s decision to move some workers to Virginia was not unexpected.

Bechtel has offices around the world, including in McLean, and one of the units moving from Frederick to Reston works with the Pentagon.

“Gaining an international company like Bechtel Corporation is a huge coup for Virginia and Fairfax County,” Gov. Robert F. McDonnell (R) said in a written statement. “The company was attracted to the commonwealth due to its business environment, cost, and ability to attract the best workforce to meet future growth needs, especially IT and engineering employees in the area.”

To lure the California-based company, McDonnell approved $6.5 million in grants: $1.5 million from the Governor’s Opportunity Fund and $5 million from the Virginia Economic Development Incentive Grant.

“It’s just another feather in our cap in Fairfax County,” said County Board Chairman Sharon S. Bulova (D). “It puts us on the map.”

Bill Dudley, Bechtel’s president and chief operating officer, said Fairfax is ideal because of its proximity to the District, the Dulles Technology Corridor, and the Reagan National and Dulles International airports.

Under the terms of an agreement reached last month with Maryland, the company is required to keep in the state 1,250 employees of Bechtel Power Corp., a division that traditionally focused on nuclear and fossil-fuel power plants but also now has a hand in several alternative energy projects.

Last month, Maryland Gov. Martin O’Malley (D) and state legislative leaders hailed a conditional $9.5 million loan to Bechtel in exchange for keeping at least 1,250 of the positions in Frederick through 2018.

According to the state’s nonpartisan budget analyst, the incentive works out to $7,600 per employee retained in Maryland. O’Malley’s administration said the cost would be recouped through an estimated $7 million in direct annual state income and sales taxes. And one official said that it worked out to less than the approximate $10,400 per-employee spent by Virginia to lure to the remaining jobs.

Some Democratic lawmakers all but acknowledged at the time that some Bechtel jobs would move out of state, and probably to Virginia. But some Maryland Republicans who had supported the loan said last week that they were surprised to learn the company would still move several hundred jobs, and they blamed Maryland’s tax rates.

In recent weeks, McDonnell has taken swipes at Maryland as not being friendly enough to business because of its taxes and regulatory policies.

Virginia officials also dialed up Lockheed Martin to see whether it might be interested in relocating after Maryland’s Montgomery County Council considered a resolution asking Congress to spend less on wars. The measure angered the company, which employs more than 5,000 workers there, and the council backed off.

Last year, Northrop Grumman chose Virginia over Maryland for its global headquarters after a process that had pitted the neighboring states against each other.

Staff writers Aaron C. Davis and Laura Vozzella contributed to this report.