That compound became Imbruvica, known generically as ibrutinib, which was approved late in 2013. It is used to treat chronic lymphocytic leukemia and some other rarer blood cancers.

Net sales of Imbruvica in 2014 were $548 million, with $492 million of that in the United States, Pharmacyclics said. Mr. Duggan predicted that sales in the United States would reach $1 billion this year. And some analysts predict that the drug will eventually reach $3 billion or more in annual sales.

The deal is the first by AbbVie since its aborted attempt last year to buy Shire, an Ireland-based drug maker. That transaction — a so-called inversion, in which AbbVie would have moved its corporate residence abroad — was driven in large part by a desire to lower its taxes.

Those deals largely stopped after the Treasury Department changed tax rules. Nonetheless, the pace of health care deals has continued to be brisk.

AbbVie needs to diversify because it now gets almost two-thirds of its sales from the drug Humira, which is used to treat various autoimmune diseases and is the world’s best-selling medicine. But Humira will lose patent protection and is expected to face competition from near-generic copies known as biosimilars in the next few years.

The company right now is not strong in cancer treatment offerings, but it is trying to create a bigger presence in that area. It is developing a drug called ABT-199 with Genentech that would treat the same types of blood cancers as Imbruvica, making it a potential competitor. However, there is some early evidence that the drugs could be used together.

Still, there are likely to be questions raised about whether AbbVie is paying too much for what is essentially half ownership of a single drug.