LONDON—European plane maker Airbus Group SE followed Boeing Co. in completing a multibillion-dollar plane deal with Iran’s state air carrier, creating another big test case for how the incoming Trump administration responds to the West’s accelerating economic opening with the Islamic Republic.

Airbus, the world’s No. 2 plane maker after Boeing, said Thursday it had completed an agreement—first announced in broad strokes in January—to sell 100 planes to Iran Air. The contract is valued at more than $18 billion based on list...