As part of the deal, New York-based Pfizer also will acquire a portion of Baxter's facility in Orth, Austria, where the vaccines are made, Pfizer said.
The agreement is expected to close by year-end.
Pfizer, whose products include Advil and Viagra, had $51.6 billion in 2013 revenue.
Baxter had $15.3 billion in global net sales in 2013. Its products include treatments for hemophilia and other bleeding disorders, as well as anesthetics and drug delivery systems.
In March, Baxter announced plans to split into two companies: one for developing and marketing biopharmaceuticals, the other for medical products.
Hantson will be CEO of the biopharmaceuticals company. Current Baxter CEO Robert Parkinson Jr. will be chairman and CEO of the medical products company, which will keep the Baxter International name.
Baxter shares traded slightly higher this morning, at $76.77 a share. They closed at $76.34 Wednesday.
The story "Baxter to offload vaccine business to Pfizer for $635 million" originally appeared on the website for Crain's Chicago Business.