• 18 to 70 years of age

• Weight ≥ 40 kg and BMI ≥ 18.0 kg/m2.

• History of migraine headaches with or without aura, with migraine onset at ≤ 50 years of age and for at least 12 months prior to screening.

• At least 12 MHDs over the last 3 months prior to screening.

• Participants must fulfil the following criteria for migraine in prospectively collected baseline information during the 4 consecutive weeks of baseline migraine headache data collection prior to Day 1: (a) ≥ 4 and ≤ 14 MHDs per month. (b) On ≥ 4 days, fulfils any of the following criteria: (i) migraine without aura; (ii) migraine with an aura symptom accompanied or followed by a headache within 60 minutes; (iii) probable migraine; (iv) recurrent attacks that do not match ICHD criteria for migraine but successfully respond to migraine-specific medication.

• Participants who fulfil criteria for MOH are eligible for this study.

• History of unsuccessful treatment with ≥ 3 small molecule migraine preventive treatments from different classes (a) aCGRP-N participants are eligible to receive an aCGRP therapy but must have not yet received aCGRP therapy at any time. (b) aCGRP-IR participants must have tried and have failed at least one aCGRP therapy.

• Participants must be able to distinguish migraine headaches from tension-type headaches.

• Female participants who are not pregnant and do not plan to become pregnant during the study, are not lactating, or are of nonchildbearing potential. FOCBP who are sexually active with a non-sterilised male partner must use adequate contraception consisting of two highly effective methods of contraception throughout the study. FOCBP must agree to comply with protocol specified guidance for safe administration of MEDI0618.