Firefighters who happened to be on a training exercise nearby also assisted in the rescue of the children, aged seven and eight, in Ilkley on Tuesday evening.
Around 100 people had congregated at the Crom Wheel 'beach' area alongside the river just before 8pm when fire crews heard screams.
The firefighters gathered their rescue equipment and ran to the scene, but found that a member of the public had already pulled the children from the water.
They were given first aid and an ambulance was called.
The younger child was taken to hospital for a check-up and was conscious and breathing at the time.
Ilkley watch commander Alex Watson said:
“This is a popular spot locally for people to congregate and on this evening there must have been around 100 people there enjoying the sunshine, children and adults alike.
“The weather we are enjoying is fabulous but please do bear in mind that despite the temperatures outside, the water can be incredibly dangerous and you can get into trouble in a split second.
“Cold water shock can take over your body and make it almost impossible to swim.
“This part of the river can look particularly inviting because it is shallow around the edges but you can quickly drift into the middle and where the river bends there are some strong currents underneath which could drag a small child away.”
On the same night, a 17-year-old boy died after getting into difficulty while swimming in the River Aire at Kirkstall.
In June 2016, a 40-year-old dad helped to rescue two brothers aged around eight and nine who got into difficulty in the same stretch of river during an evening swim.