It was taken by ex-students and staff from UWC Atlantic College in the Vale of Glamorgan who also stayed to help.
The boat will be used to try to ensure the safe landing of boats from Turkey.
A narrow stretch of water has become a crossing point for people from Syria and other countries which has claimed many lives.
College alumni Robin Jenkins and Lily Eckersley-Jones helped transfer the rescue boat to Lesbos with college tutor Michel Creber where another former student, Dr Annegret Berne, had been volunteering.
Mr Jenkins, originally from Llantwit Major and a lecturer at University of the Arts London, said: "The faces of the people on board when we come alongside is something that I cannot put in to words.
"We were a reassuring sign of safety.
"We must do more and we will start on constructing another boat."
The first vessel, named LB1 Red Mist, had formerly been used by the college at St Donat's, near Llantwit Major, and its students before being sent to Lesbos.
It is now being used by a group called the Lifeguard Hellas Training Centre.
Its design is the same as the original rigid hull inflatable boat (RIB) made in the early 1960s by students from the college and which has become the model for RNLI inshore boats across Britain - known as the Atlantic class.
Mr Jenkins set up a help group called the Atlantic Pacific Rescue Boat Project to deliver a boat to Japan to assist lifeguards and now others are being made to help rescuers in Lesbos.
He said college students working with tutor Michel Creber have already began work on a second RIB and he had also received a donation on Tuesday to cover the cost of making a third.
A Welsh lifeboat has been sent to Lesbos to help people trying to ensure the safety of refugees and migrants arriving by boats on the Greek island.