It is likely that they learned of Sauron's demise and departed for Valinor.

^ No evidence of this.

The only thing that is written is that the went into the east and the south and very little is heard of them after that Mandos probably knows, but he didn't tell us.

@Fandyllic I edited the comment to fix this.

@Fandyllic The original post by KaraZorElisLongPig asked what people believed happened to them. Tolkien may not have written about the ultimate fate of the Blue Wizards, but people can have headcanons and speculate about the ultimate fate of the Blue Wizards.

...and? I just said there is no evidence of that. If people are going with headcanon, they should say that.

I believe that they were killed at some point before completing their mission.