Tolkien went through several different ideas on how Elvish death and immortality worked, but this is the one that made most sense to me. The basis is the short piece 'The Converse of Manwë and Eru' in 'Morgoth's Ring'.
Also, in 'Laws and Customs of the Eldar' it says, "Only those return whom, after Mandos has spoken the doom of release, Manwë and Varda bless". It's not clear whether Manwë and Varda possess this authority jointly or severally, though. Or maybe Manwë does the men and Varda does the women, or vice-versa.
Part 121: What dreams may come
Next time: Part 122: Judge of the Dead
Chibis by tektek.org
PS: Yes, it's canon that God is slightly snarky about the Valar summoning the Elves to Valinor. Tolkien's actual text is,
Eru answered: "Have I not given to the Valar the rule of Arda, and power over all the substance thereof, to shape it at their will under My will? Ye have not been backward in these things. As for my First-born, have ye not removed great numbers of them to Aman from the Middle-earth in which I set them?"