The people on board the moving bus, who were mostly elderly, were thrown forward by the force of the unexpected impact.
Police said five passengers suffered serious injuries and were rushed to the Dorset County Hospital by ambulance.
Paramedics treated 13 more at the scene for injuries ranging from broken bones, cuts and bruises and severe whiplash.
Of the ‘walking wounded’ seven were taken to a local minor injuries unit to be treated and the remaining six were tended to at the scene by paramedics..
Several of the injured were fitted with neck braces, including the driver of both buses.
There were no reports of any people being trapped.
A large panel of safety glass on the side of the bus popped out on impact and showered the pavement and a nearby shop with splinters of glass.
Police declared the collision, that happened at 10.37am today, a ‘major incident’ which involved four ambulance, four fire engines and a small fleet of police cars.
An investigation has been launched into the collision and one line of inquiry is that the bus driver’s foot slipped on to the accelerator as the vehicle pulled in to the bus stop.
An office worker who witnessed the aftermath of the collision said: ‘I heard a really loud bang and looked out and saw these two buses conjoined together.
‘The first bus had been stationary at stand K3 and was picking up passengers to go to Dorchester and the second bus came in behind it and hit it hard.
‘There were lots of people on the street rushing around with tissue and handkerchiefs and bottle of water.
‘The emergency services got here very quickly and helped off most of the passengers off both buses.
‘They looked mostly elderly and needed assistance. I saw some with their arms in a sling and some in neck braces and a few with a bloody nose.
Inspector Matt Butler, of Dorset police, said: ‘The collision involved one of the buses striking the rear of the other.
‘It was declared a major incident and all three emergency services attended.
‘There were five people who were seriously injured and they were taken to the Dorset County Hospital. Seven people were walking wounded and attended a minor injuries unit it Weymouth and six others had minor injuries that didn’t require further treatment.
‘We are investigating the cause of the collision and are appealing for witnesses.’
In total two ambulances and two paramedic cars attended the incident along with four fire engines.
The collision occurred on the Esplanade in Weymouth which had to be closed for more than three hours.
Both buses are run by the First Bus group.
Simon Newport, of First Dorset, said: ‘We can confirm that at around 10.40am two of our vehicles were involved in an incident at the Weymouth Esplanade bus stop in Weymouth.
‘Our thoughts are with those that were injured as a result of the incident.
‘We have launched a full investigation to establish exactly what happened and are working closely with the emergency services.’