Shire, which employs 5,300 people in 29 countries, will merge its operations with AbbVie, the maker of rheumatoid arthritis treatment Humira, as long as shareholders approve the tie-up later in the year.
Founded in 1986 by a group of five scientists, Shire is best known for its attention deficit disorder drugs. It is listed on the London Stock Exchange, has its tax base in Dublin and sells most of its products in North America.
In the UK, Shire employs 500 staff between sites in Basingstoke and Maidenhead, where work is carried out on some of the firm's biggest selling drugs such as treatments for Attention Deficit Hyperactivity Disorder (ADHD) and rare diseases such as Hunter Syndrome and Fabry disease.
AbbVie's pursuit of Shire started in early May, at the same time as AstraZeneca was fighting off interest worth £69 billion from drugs giant Pfizer.
The pharmaceuticals sector has seen a raft of deal-making activity in recent months as US companies look to Europe as a way to reduce their tax liabilities.
The Illinois-based firm said it plans to move its domicile to the UK in a move that would cut its corporate tax rate.
The company was formed in January 2013 after it was spun off from Abbott Laboratories. It employs around 25,000 people worldwide and markets medicines in more than 170 countries.
AbbVie had until today to confirm an offer for Shire, having increased its offer price from 4626p a share, or £27.2 billion, in May to a cash and shares proposal worth 5248p a share, equivalent to £30.9 billion.
Shire chairman Susan Kilsby said the price reflects the "substantial value" that the company has created for shareholders and also its future prospects.
She added: "We believe that the combined group represents an exciting fit of two complementary businesses.