Abbott Laboratories said on Monday that it had agreed to sell its established generic drug business outside the United States to the generic drug maker Mylan in an all-stock deal that valued business at about $5.3 billion.

Under the deal, Abbott will take a 21 percent stake worth about $5.3 billion in a new company that combines Mylan’s existing business with Abbott’s developed markets pharmaceuticals operations in Europe, Japan, Canada, Australia and New Zealand.

The transaction will allow Mylan to engage in a so-called inversion: the Pennsylvania company would reincorporate in the Netherlands to lower its corporate taxes and to free up cash held in overseas entities.

Mylan, whose headquarters are in Pittsburgh, unsuccessfully pursued the Swedish drug maker Meda this year in hopes of engaging in an inversion.

“We have been actively looking at a wide range of opportunities, and the acquisition of this business is absolutely the right next strategic transaction for Mylan as it builds on our strong momentum, expands and further diversifies our business in our largest markets outside of the U.S.,” Robert J. Coury, the Mylan executive chairman, said in a statement.

Inversions have spurred a series of mergers this year, particularly in the pharmaceutical sector.

On Monday, Shire, an Irish drug maker, said its board, pending further discussions, was willing to recommend a $53 billion takeover offer from AbbVie, which spun off from Abbott last year. AbbVie would reincorporate in Ireland as part of the merger.

The generic drug business that Abbott is selling operates in Europe, Canada and parts of the Asia-Pacific region, and it has about 3,800 employees. It has manufacturing facilities in France and Japan.

The business has a portfolio of more than 100 specialty and branded generic pharmaceutical products in five therapeutic areas, including cardiovascular and gastrointestinal treatments.

The deal, which is expected to close in the first quarter of 2015, would roughly double Mylan’s revenue in Europe and generate additional annual revenue of about $1.9 billion, Mylan said.

Mylan, founded in 1961, sells generic and specialty drugs in about 140 countries and employs about 20,000 people. The company posted revenue of $6.9 billion in 2013.

Abbott, based in Chicago, will retain its generic pharmaceutical business in emerging markets and other businesses in developed markets.

After the transaction, Abbott said it would focus its generic drug business on emerging markets where there is a greater opportunity for growth. The business that remains with Abbott had revenue of about $2.9 billion in 2013.

“This transaction provides Abbott with additional strategic flexibility as we continue to actively manage and shape our portfolio, reflecting our commitment to long-term, durable growth,” Miles D. White, the Abbott chairman and chief executive, said in a statement.

Abbott said it did not intend to be a long-term shareholder in Mylan and would seek to sell its stake in the future.

Abbott posted revenue of $21.8 billion in 2013. The company operates in more than 150 countries and employs about 69,000 people.

Morgan Stanley advised Abbott on the transaction. Centerview Partners and the law firm  Cravath, Swaine & Moore advised Mylan.