The nursery, based in the grounds of Ninewells Hospital, offers 92 places to children aged between 3 months and 5 years, and employs approximately 40 staff.
Headquartered in Staffordshire, Busy Bees is the largest childcare provider in the UK which, including this acquisition, now operates 267 nurseries.
The firm currently employs over 7,700 staff and providers care for over 30,000 children.
Busy Bees is now keen to expand further in Scotland, with the Dundee nursery taking the group to 17 nurseries across Scotland.
Marg Randles, managing director, said: "We are delighted to welcome The Teddy Bear Club into the Busy Bees family. The nursery has a fantastic reputation for providing quality childcare in Dundee and we can’t wait to start working with such an exceptional team.
"We will be working very closely with the management team to make this transition as seamless as possible for everyone involved.
"We will ensure that our parents are kept up-to date throughout the transition process, as we continue to improve the excellent care, resources and services The Teddy Bear Club currently provides."
Angela Gatford, founded The Teddy Bear Club Nursery in 1998. She said: "It was with some sadness, that I came to the major business decision to sell The Teddy Bear Club Nursery. It has over the last 18 years, been caringly managed for me, by Susan Gorman and Jacqui Lowson.
"I am very proud of the Nursery’s constant excellent reputation, which is down to the hard working Management and staff over the past years.
"I am very happy that all the present staff will be remaining, to continue to care for the children to the highest of standards. I would like to pass on my thanks to all my staff and parents past and present for all their loyalty over the years.
"I am positive that the staff and children will benefit from the new investment and experience that Busy Bees will bring with them, and wish them all, every success."