Jeremiah Deen lived on the 14th floor of the west London block with his mother Zainab, 32, who had already been confirmed as one of the deceased.
The toddler is the 45th victim of the 24-storey blaze, which killed at least 80 people on 14 June, to be formally identified.
The Deen family said the mother and son would "last a lifetime in our hearts".
Baby Logan Gomes, who was stillborn in hospital on 14 June, has also been recorded by police as a victim of the fire.
Ms Deen's parents released a statement announcing the death of their daughter and grandson, which said: "We would like to express our heartfelt appreciation to all relatives and friends for their prayers, floral tributes and expression of condolences during this difficult time.
"Funeral arrangements will be announced later as plans are being made to lay mother and son to rest.
"You spent a moment in our arms, but you will last a lifetime in our hearts."
On Monday the Metropolitan Police confirmed that 12-year-old Jessica Urbano Ramirez was also one of the victims of the fire.
Nura Jemal, 35, was also named by the force.
A two-year-old boy is the latest person to be formally identified as a victim of the Grenfell Tower fire.