Moyles Court Wildlife Rescue Centre was called out early on Sunday morning after concerned members of the public and police reported the cygnets on the road.
Dorset Police contacted the rescue centre after a swan was spotted at Ashley Heath roundabout, near Ringwood.
Meanwhile, Hampshire police called the centre about two more swans on the A31 at Poulner Hill.
A spokesperson for Moyles Court Wildlife Rescue Centre said the team “set off immediately” to help.
Swans rescued from the A31 (Image: Moyles Court Wildlife Centre)
They first attended the swan at Ashley Heath before travelling through the resulting traffic tailback to Poulner Hill.
Hampshire Police had already managed to catch one of the swans, leaving the rescue team to catch the remaining cygnet.
The three young swans were taken to the wildlife hospital, where staff confirmed they had escaped the incident without injury.
The spokesperson said: “Luckily none of these three young swans (cygnets) were injured and they are now all safely here at our Wildlife Hospital.
“We would like to take this opportunity to thank both Hampshire and Dorset Police for their continued support with numerous roadside wildlife rescues.”
The rescue centre said the incident had caused “early Sunday morning traffic mayhem” on the A31.