A joint venture led by L.A. real estate investment trust Hudson Pacific Properties Inc. has completed its acquisition of the second building in Burbank’s Pinnacle office complex, the company said Wednesday.

The 231,864-square-foot building, at 3300 W. Olive Ave., was built in 2005 by Los Angeles developers M. David Paul & Associates and Worthe Real Estate Group, who are members of the acquiring joint venture.

The new arrangement reduces M. David Paul and Worthe’s interest in the project to 35 percent. Hudson Pacific has a 65 percent interest in the joint venture, which acquired the two properties for a total of $342.5 million.

The Pinnacle II is 100 percent leased to Warner Bros. Entertainment. The Pinnacle I, at 3400 W. Olive Ave., is 92 percent leased and tenants include radio station KIIS-FM and Warner Music Inc.

“The Pinnacle provides Hudson with an immediate foothold in one of the top media and entertainment submarkets in Los Angeles,” said Victor Coleman, Hudson’s chairman and chief executive, in a statement.

Hudson Pacific went public in June 2010 in a $218-million initial offering. It is led by Coleman, who was previously chief operating officer at Arden Realty Inc. before it was acquired for $3.2 billion by General Electric Co.

Hudson’s portfolio includes the Sunset Gower Studios and the Sunset Bronson Studios in Hollywood, along with the First Financial office building in Encino.