Klaus Kibsgaard will take over as BMW UK MD, while O’Donnell will take up his new role in America on April 1.
Kibsgaard has been president of BMW Portugal since 2003. He said: "I am thrilled to be offered the opportunity to manage BMW’s third largest market.
"Jim and the management team at BMW UK have done a terrific job culminating in 2007’s record results. I hope to carry on from this high level and further the successful record for the BMW and Mini."
O’Donnell takes over functional responsibility for US activities, he said: "I will miss my colleagues and, of course, the dealers who have helped to build our success in the UK.
"I am proud of our results and optimistic that Klaus will take BMW UK to new highs. He is inheriting a strong and committed group of employees and I will watch the UK’s progress with interest."
Klaus Kibsgaard will start his role as BMW (UK) MD on March 1.