ïnspector Diane Davies, of Dyfed Powys Police, said: "This is a terrible tragedy and my heartfelt sympathies go to Mr Jack’s family as well as individuals who witnessed the incident and valiantly tried to save him."
Residents were alerted to the tragedy by emergency vehicles arriving at the scene.
Betty Pugh, who lives nearby, said: "The water at that spot is very deep and very cold.
"The man had managed to rescue the girl. He had her in his arms and passed her to people on the bank."
Police and paramedics were joined by fire crews from Machynlleth and Aberystwyth. RNLI crews at Aberdyfi and Borth were also put on standby but did not launch.
A Welsh Ambulance Service NHS Trust spokesman said: "We were alerted at 5.44pm to the incident. We had two ambulances at the scene. A male adult was declared deceased at scene. A child was looked after by paramedics."
Officers launched an investigation into the circumstances surrounding Mr Jack’s death but it is not being treated as suspicious.
The Powys coroner was informed.