The deal is anticipated to close by the end of this month, earlier than scheduled.
Galapagos will receive an upfront payment of $725m, which includes a license fee of $300m.
Gilead will make a $425m equity investment in Galapagos by subscribing for shares at a price of €58 per share.
Once the shares are issued, Gilead will own about 15% of the outstanding share capital of Galapagos, based on the dollar to euro exchange rate at closing.
Galapagos is also eligible for payments about $1.35bn in milestones, with tiered royalties beginning at 20% and a profit division in co-promotion territories.
Filgotinib is a highly selective JAK1 inhibitor discovered and developed by Galapagos using its target and drug discovery technology platform.
Phase 2 trial data demonstrated that filgotinib has the potential to be an effective and well-tolerated oral therapy for patients with rheumatoid arthritis and Crohn’s disease.
The companies will start phase 3 trials in RA and Crohn’s later this year after the successful outcome of negotiations with regulatory authorities.