Barney, who's appointment is effective immediately, will operate out of Hong Kong and Mumbai, the company said in a statement.
Punit Garg, who was the President and CEO of Reliance Globalcom since January 2006, will lead the Indian enterprise business of RCom.
"We are delighted to have Bill join us to lead Reliance Globalcom into an accelerated phase of growth and development, leading to enhanced unlocking of value for the benefit of all our stakeholders," Reliance Communications Chairman Anil D Ambani said.
"We are at an important time in the evolution of global Internet technology and I look forward to working with the team to further advance the company's position in the global marketplace," Barney said.