Alder's Randall Schatzman said he hoped to submit licensing applications for public use in 2019.
The firms are developing variants of a drug that tackles a protein called calcitonin gene-related peptide (CGRP), which triggers the pain and nausea of migraines. It causes the swelling of blood vessels intertwined with nerve endings on the side of the head.
Researchers found antibodies engineered to bind to CGRP were able to "mop up" the chemical, meaning it did not trigger a migraine.
Scientists realised the significance of CGRP in the 1980s, but earlier trials were abandoned over fears that they caused liver damage. The latest batch of drugs have shown few safety issues, according to the trial results.
Amgen's Sean Harper told the Financial Times: "I can think of only a few examples of holy grails in medicine, which have existed for thousands of years, and this is one of them."
Eli Lilly reported a significant reduction in the number of "migraine days" for patients who took the drug last June. Teva, an Israeli drugs firm, reported similar results for its own drug in September.
Peter Goadsby, neurology professor at King's College London and trustee of the UK Migraine Trust, said of the trials: "This is a huge development for migraine sufferers ... For a group of people who have never had a proper treatment, this is fantastic news."