Big sister Libby was born in May 2008 but was only joined by her siblings Neeve and Maddie earlier this month.
All three girls were conceived at the same time during IVF treatment despite their parents, Nadine and Martin, being warned by doctors they might never have children.
"It's a bit surreal having triplets who are different ages but we can already see the resemblances between them," Nadine, 38, told the Daily Mail.
"When we started fertility treatment I never imagined we would have one child, let alone three. It's a dream come true."
The couple tried for 18 months to have children naturally but eventually paid £6,000 for private IVF.
Six embryos were created and one was implanted immediately, while another four were frozen for possible use in the future.
Nadine, from Melksham, Wiltshire, became pregnant at the first attempt and had Libby, now three. She then had two further embryos implanted last June, to increase her chances of a successful pregnancy.
"The doctors told us there was just a 14 per cent chance of one of those embryos being viable," she told the newspaper.
"They didn't give us any odds for both embryos taking, as it's thought to be less than one per cent.
"Martin and I were very aware that we might not be so lucky this time and we tried not to get our hopes up too much."
But the couple were astonished to learn Nadine was expecting again – and even more amazed to find she was expecting twins.
"We were overjoyed," Nadine said. "We'd struck lucky twice with the IVF treatment and now we were having not one but two babies. The nurses were smiling and saying 'What's your secret?'. It was more than we could ever have asked for."
Maddie and Neeve were born on February 5, four weeks early, weighing 5lbs 8oz and 4lbs 12oz respectively, and were allowed home two days later.
Their mum and dad say they will tell their non-identical triplets about their special relationship when they are older.
We're still trying to get our heads round the fact we've got triplets who are different ages but it's lovely to see people's reactions," said Nadine.