The real answer to this question is quite simple and pretty straightforward.
Sir Thomas More in his The History of Richard III says it was so.
but here's the interesting bit......
"Whiche after that the wretches parceiued, first by the strugling with the paines of death, and after long lying styll, to be throughly dead: they laide their bodies naked out vppon the bed, and fetched sir Iames to see them. Which vpon the sight of them, caused those murtherers........... to burye them at the stayre foote, metely depe in the grounde vnder a great heape of stones....... Than rode sir Iames in geat haste to king Richarde, and shewed him al the maner of the murther, who gaue hym gret thanks."
The 'story' that the remains are of Edward and Richard, stems partly from the work of Professor William Wright and Dr. George Northcroft who published their findings in ‘The Sons of Edward IV. A re-examination of the evidence on their deaths and on the Bones in Westminster Abbey’ This work ought to be treated with caution, DNA aside, I wonder how it can be suggested that they were, in life, the princes, if they never established the sex of the skeletons? In 1986 it was pointed out that a couple of important facts from the study were not mentioned. Firstly, there were indications in "existing and unerupted teeth" that suggested that one of the skeletons was a female, and secondly, the age gap between the two remains was less than three years between the birth of the princes.
IF these two boys met their deaths at the Tower, who in their right minds would place the bodies under the noses of all who were in the present at the time, without being seen and within a limited time frame? Others feel the same, suggesting there were better ways to get rid of the bodies than to hide them somewhere in the Tower itself.
I don't know why More wrote what is written here, or what his motives were, I don't know what happened to the two princes in the summer of 1483, they may well have been murdered, but equally, they might not have been.
What I do know is that it has never been proved that the two sons of Edward IV were dead at all.
I also don't believe it is their remains at Westminster Abbey.