Lucas Walker was playing when he was swept away on Saturday.
His mother, 37-year-old Julie Walker, tried to save him, but both died. His brother Samuel, 13, and bystanders also tried to help.
Relatives said in a statement that they were "understandably devastated" by the tragedy.
It read: "Julie was a kind and loving mother who would have done anything for her children, while Lucas was a lively and energetic little boy who was inquisitive by nature.
"We would like to express our heartfelt thanks to the emergency services who assisted at the scene, and would also like to say how grateful we are to the members of the public who entered the water that day to help.
"We would also like to take this opportunity to thank everyone for the countless messages of support we have received. We can take great comfort from them at this extremely difficult time.
"As a family we now have to come to terms with our devastating loss."
Lucas was a pupil at Bramble Brae School in Aberdeen.
His brother was also pulled from the water, along with a man and a woman who had also tried to save the pair.
The emergency services were alerted to the incident at about 16:45 on Saturday.
Relatives of a mother and her six-year-old son who died after getting into difficulties at Aberdeen beach have thanked those who tried to rescue them.