NorthStar Realty Finance Corp. agreed to buy Griffin-American Healthcare REIT II for about $3.4 billion, expanding its holdings of medical-office buildings and senior housing.

Stockholders of Griffin-American, a real estate investment trust that isn’t traded on exchanges, will receive $11.50 a share, comprising $7.75 in cash and the rest in NorthStar common stock, the companies said Tuesday in a statement. NorthStar also will assume about $600 million of debt.