Walsh, who was previously chief executive of British Airways, had been due to step down in June, but stayed on to oversee IAG during the Covid crisis.
Gallego said: “It’s an honour to become IAG’s chief executive, following in Willie’s footsteps and building on all that he has achieved in the past nine years.
“This is a hugely difficult time for our industry. Not only do we face the immediate challenge of Covid but we must ensure that IAG is strong and resilient when it emerges from the crisis.