NEW YORK (Bloomberg)—Johnson& Johnson agreed to pay $1 billion for a stake in Elan Corp. and will develop the Irish drugmaker’s medicines against Alzheimer’s disease.

J&J, the world’s biggest health-care company, will get 18.4 percent of Elan and create a new unit to hold the Alzheimer’s medicines that Elan is developing with its partner Wyeth, the companies said Thursday.

Wyeth agreed in January to be acquired by Pfizer Inc., the world’s biggest drugmaker, in a deal set to close by year’s end.

The agreement gives New Brunswick, N. J.-based J&J rights to bapineuzumab, one of the most advanced Alzheimer’s drugs in development. Drugmakers have raced to cultivate treatments for Alzheimer’s as the number of patients with the brain-wasting condition is set to double to 34 million within 16 years, according to the Geneva- based World Health Organization.

The drugmakers will close the transaction in the second half of the year. Both boards have approved the deal.