Max Simmons was hit by a Red Audi TT on Switchback Road North in Maidenhead, Buckinghamshire, at 1.25pm on Saturday.
The driver, 34-year-old James Lavine, of nearby Woodburn Green, has since been charged with causing death by dangerous driving.
Max's mother - who has not been named - said in a statement on Sunday: "Thank you for all the kind messages that have come through.
"It means a lot to know how much other people loved him. I always taught my kids to be street smart but brave and independent."
She added: "Whilst I have the chance I'd like to thank all the doctors and nurses and staff at the John Radcliffe Hospital - it's people like them that keep the NHS alive, and they worked as hard as they could to save my boy. Thank you all.
"From one parent to all you parents out there, go home and hug your children. Just be there with them, hug them, tell them how much you love them, because Christmas presents are just stuff, love is free. Just love each other."
Max is survived by one brother.
Lavine is due to appear at Slough Magistrates' Court on Monday.