Mr Fisher, 44, will take up a position as co-chief executive of the Belgium-based company, in which private equity firm Ripplewood Holdings hold a controlling share.
It is thought Mr Fischer, who had only fairly recently been appointed to the position with Credit Suisse, will be charged with assisting Ripplewood acquire financial services companies and will oversee a team of 40 people.
Commenting on today's appointments, D. Ronald Daniel, chairman of RHJI, said: "The board of directors is very pleased with today's announcements, Leonhard is one of the most respected executives in Europe.
"His talents are very complementary to our existing leadership team and we believe he will be instrumental in RHJI's pursuit of its global investment strategy," he added.
Prior to his departure, speculation had been rife that Mr Fischer would go on to succeed current Credit Suisse chief executive officer Oswald Grubel.