His spirit passed out "of time and space" (i.e. completely out of the created universe) before it was sent back.  Gandalf also receives a new body -- which is somewhat different from the old one; hence Strider, Legolas, and Gimli don't immediately recognise him when he reappears.  In his letters also Tolkien explicitly says that Gandalf died; and adds that it was Ilúvatar Himself Who sent Gandalf back.  Basically, Gandalf made the ultimate sacrifice for his friends: he had no idea that Ilúvatar would send him back.

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All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.