Brookfield is building a deck above the train tracks leading into Penn Station at Ninth Avenue and 33rd Street. Steve Remich for The Wall Street Journal

Brookfield Property Partners LP has signed a lease with a digital advertising firm to take a large swath of space at Five Manhattan West, a deal the company said reflected growing momentum for its planned campus of office and residential towers on the far West Side.

R/GA Media Group Inc. will take 173,000 square feet, moving its offices to the entire 12th floor and part of the 11th floor of the building, Brookfield said. The lease is the first signed at the tower since February, when Brookfield unveiled plans for a $200 million overhaul of the 1969 structure at 450 W. 33rd St.

R/GA, a subsidiary of the Interpublic Group of Cos., didn't return requests for comments.

Brookfield officials declined to discuss financial details, but the range of asking rents at the building has risen from the high $60s earlier this year to levels between $78 and $80 a square foot, said Jeremiah Larkin, executive vice president and director of leasing for Brookfield.

"This will be the newest neighborhood where you can live, work and play, and people are recognizing that," he said. "Rents continue to rise, so tenants are jumping on it."

The property at 450 W. 33rd Street Steve Remich for The Wall Street Journal

The 1.8-million-square-foot building has about 300,000 to 350,000 square feet of space available with serious interest from potential tenants for almost all of it, Mr. Larkin said. Brookfield acquired the 16-story tower in 2011 and plans to give it a new, glass exterior and unobstructed floor-to-ceiling windows.

The building will be incorporated into Brookfield's planned 7-million-square-foot campus called Manhattan West. That complex will have a residential tower, two office buildings, a hotel and 200,000 square feet of retail space. Two acres of landscaped public space will sit at the center of the campus. A significant piece of the project is a platform Brookfield has been constructing over part of the rail yards west of Penn Station using technology usually employed for building bridges.

The renovation, shown in a rendering, will be renamed Five Manhattan West. Brookfield Property Partners

Brookfield is one of several developers with plans to build on Manhattan's far West Side and transform the area with shopping, offices, residences and hotels. Hudson Yards, the Related Cos. venture, includes more than 17 million square feet of commercial and residential buildings and 14 acres of public open space.

The "epicenter" of Manhattan's office market "is beginning to shift to Midtown West, Midtown South and Downtown," said Bruce E. Mosler, chairman of Cushman & Wakefield Inc.'s global brokerage and part of the team representing Brookfield. That movement largely has been driven by tenants such as R/GA in the technology, advertising, media and information-related business sectors, Mr. Mosler said.

Tenants in these industries accounted for about 22% to 23% of Manhattan's office space compared with 30% for those in the financial services, as of the first half of the year, said Ken McCarthy, Cushman & Wakefield's senior managing director of economic analysis and forecasting.

Brookfield won't begin construction of its office towers in the Manhattan West project until it finds anchor tenants. But Mr. Mosler expects the makeover of Five Manhattan West to boost that effort.

"This gives tremendous credibility to the project overall because it speaks to the quality of what Brookfield is building," he said.