Dean Price went into the River Esk at Longtown after his seven-year-old daughter, Delilah, slipped and fell into the water on 30 June.
The 32-year-old, from Walsall, got into difficulties and disappeared. His body was found hours later following an extensive search of the river.
The South Cumbria coroner recorded a verdict of accidental death.
Geoff Maxwell, an off-duty retained firefighter who was working nearby, managed to rescue the girl.
He was praised by coroner David Roberts, who said: "On behalf of the public generally, I would like to thank you for your selfless act."
A man drowned while trying to rescue his daughter from a river in Cumbria, an inquest has found.