The deal follows last month's news that the future of the agency was in question after its parent company in Sweden filed for bankruptcy.
Charlotte Neser, the managing director of Abel & Baker UK, and the agency's core UK creative team, will be kept on to run the agency. However, four of the agency's nine staff have lost their jobs in the move. Abel & Baker will continue to operate under its existing name, but will relocate to Wheel Group's Kensington offices.
Wheel Group, the online marketing services agency trading under the brand names Wheel and Foresight, acquired the rights to the Abel & Baker brand name for an unspecified sum.
Philip Hunt, the chief executive of Wheel Group, said: "This is an important acquisition which will accelerate the development of our interactive marketing services offer. Since launching in February 2001, Abel & Baker has established a leading reputation for creative campaigns."
Neser added: "This deal offers us the opportunity to build on the work we've done with clients and partners in the UK over the past year."