Cannot find any origin story for the world tree on wikipedia. Was it created from the body of Ymir too?
Yggdrasil doesn't seem to have an origin; in the Prose Edda, which is a compendium of Norse myth, we get a description of the various beings that live in and around the tree, and how its three roots extend across the cosmos, but nothing about how it came to be. (You can find a pdf of Faulkes' translation here, or an older one on this page.)
It doesn't seem unreasonable to suppose that it has always been there, since in the poem Voluspa, which tells of the creation and destruction of the world, Yggdrasil also just exists, and may possibly have survived the fatal battle of gods and giants.
Two humans survive the cataclysm, Lif and Lifthrasir, by hiding in "Hoddmimir's holt", and if he is the same as Mimir who owned the well at the foot of the tree, then we have to assume the tree survived as well.
In Völuspa 2, when describing how she was fostered by giants in the beginning of time, the völva says that she remembers "mjötvið mæran, fyr mold neðan" (the glorious measuring-tree in the earth below). This probably means that the world tree sprang from the ground as the world was created.