Philip Garvey, 56, his wife Ann, 55, their daughter Emily, 23 and son Daniel, 20, all from Surrey, died in the crash near Churchinford.
"They were the best family anybody could have wished for and they brought happiness to everyone they met," a family statement read.
An investigation into the cause of Saturday's crash is under way.
The family from Woking, had been flying towards Dunkeswell Aerodrome in east Devon.
Relatives of four people who were killed in a plane crash in Somerset say they are "utterly heartbroken".