Malkin and Rockliffe replace Kate Triggs, who quit almost eight months ago (PRWeek, 10 September 2004) to join Edelman.
The duo share the title of joint MD and take charge of a UK team that is around 30-strong.
The pair - who have been co-managing the practice since Triggs's exit - report to UK CEO Per Heggenes, who said: 'We couldn't find anyone better.
They have both proved themselves as leaders.'
Heggenes conceded that he had 'talked to a good proportion of people in the market', adding: 'It is a tight market to recruit in.'
Malkin was already an MD before Triggs's exit, while Rockliffe - a med ed specialist - has been promoted from a director role.
B-M has also appointed Camilla Dormer as a director (health). She joins next month from a France-based role as press and PR officer at the European Society of Cardiology and will sit alongside health directors Ellen Sarewitz and Monica Shuman.
Malkin has worked at B-M for a decade, having joined in her native New York in the mid-1990s.
Rockliffe joined B-M two years ago from Adelphi Communications.
B-M has healthcare clients such as Pfizer, GlaxoSmithKline, Lundbeck and Ortho Biotech.
Dormer has been replaced at the European Society of Cardiology by Gina Dellios, who has joined from a job as external relations manager at France's Theseus International Management Institute.