Abbott Laboratories’ deal to acquire medical-products maker St. Jude Medical Inc. for $25 billion was the largest in a flurry of health-care deal-making Thursday that could total more than $40 billion.

France’s Sanofi SA said Thursday it made an unsolicited, $9.3 billion offer to purchase San Francisco-based Medivation Inc., which sells a lucrative prostate-cancer drug. AbbVie Inc. of North Chicago, Ill., agreed to pay $5.8 billion, plus up to an additional $4 billion in potential future payments, to acquire privately held...