Hazil Rahaman-Alan, 39, was sentenced at the Old Bailey after he admitted having the grenade with intent to endanger life and having a dangerous article on a plane.
Judge Gerald Gordon recommended that Rahaman-Alan be deported to his native Venezuela after serving his sentence.
Rahaman-Alan was not a terrorist but suffered from depression, the court was told last month when he entered his pleas. The court heard his grenade could not explode because the detonator was missing.
However, the discovery of the grenade forced the evacuation and closure of the airport's busy North Terminal for six hours.
Rahaman-Alan told police he wanted to blow himself up in an open area, possibly a park, because he wanted to help humanity and the plight of the world's children.
Nicholas Dean QC, prosecuting, said: "He said the grenade would be his microphone to the world."
