"We grieve the loss of our beautiful, loving daughter and sister," the Archibald family said in a statement as quoted by the Telegraph newspaper.
The media added that the second victim is known to be from France. The authorities are yet to officially name the seven victims.
On Saturday, at 22:08 local time (21:08 GMT), a vehicle struck pedestrians on London Bridge. The vehicle with three suspects continued to drive from London Bridge to Borough Market, after which the suspects left the vehicle and carried out a stabbing attack at the market. The attackers were confronted by the police and shot dead within minutes.
According to the local authorities, at least seven people were killed and 48 more injured.
A total of 12 suspects, including four women, have been detained over the attack.