Karen Rodger, 41, and husband Colin, 44, from Langbank in Renfrewshire were "over the moon" at the new arrivals to their family on May 29 at the Southern General Hospital in Glasgow.
The girls, who are not identical, were delivered by caesarean section with Rowan arriving first weighing 5lbs 8oz and two minutes later Isla weighing 6lbs.
The couple already have four boys - 14-year-olds Lewis and Kyle and Finn and Jude who are both 12 - and were told of the unlikely odds that Mrs Rodger's third pregnancy would be twins.
She said: "I just could not believe it. It never crossed my mind that it would be twins again, I just thought that just doesn't happen to people like me but I'm absolutely delighted."
Mrs Rodger found out during a scan six weeks into the pregnancy and sent a text with the news to her husband.
"He thought I was joking and immediately wrote back to say 'this is not funny'. I had to explain that it really was true," she said.
"I still haven't really taken it on board because I was convinced I was having two boys."
The couple are looking to convert the loft of their house into bedrooms for their eldest twins so that the girls can have their own room.
Mr Rodger described the arrival of the twins as "life-changing" and said he was looking forward to raising daughters.
"Boyfriends will be completely unacceptable.