As Gandalf says on a number of occasions:
Olorin I was in my youth in the West that is forgotten.
They definitely have knowledge of what they are and where they came from, but despite that their memory does seem to be a little dimmed. After Ilúvatar sends Gandalf back we also see him saying:
I have passed through fire and deep water, since we parted. I have forgotten much that I thought I knew, and learned again much that I had forgotten.
Tolkien isn't clear on what those things Gandalf had forgotten and learned again actually are, so we need to look to the Istari material in Unfinished Tales for more information:
For it is said indeed that being embodied the Istari had needs to learn much anew by slow experience, and though they knew whence they came the memory of the Blessed Realm was to them a vision from afar off, for which (so long as they remained true to their mission) they yearned exceedingly.
So the basic answer is therefore "yes": they do have knowledge of their past and awareness of their former lives, but it's not a perfectly clear recollection.
It may of course be assumed that Gandalf post-resurrection is a special case: Tolkien notes in various Letters (e.g 246) that it was Gandalf who interceded with the Valar to allow Frodo and Bilbo go West at the end:
No doubt it was Gandalf who was the authority that accepted her plea.
This definitely implies that following his return and the defeat of Sauron, he was able to establish some kind of contact with Valinor that he had not before.