Sixty five-year-old Stange's-year-old career includes leading Belarus during the UEFA Euro 2012 qualifying campaign where they defeated France in an away qualifier. The country saw its FIFA ranking rise to 36 in 2011, from 90th place in 2008.
Under his watch, Belarus saw victory over the Netherlands and draws against traditional football powerhouses Germany and Argentina.
"The post of National Team Head Coach is always a challenging one for any coach – more so in a country like Singapore where football is the number one sport and whose national team are now champions of the region," said Stange, who also coached Iraq and the former East Germany.
"I am deeply honoured to have been appointed from a pool of more than 100 qualified candidates."
President of the Football Association of Singapore, Zainudin Nordin, described Stange on Wednesday "one of the most respected coaches in Europe today."
He said the German "brings with him a wealth of international experience, ability and track record of building and managing successful teams despite the constraints."
Stange replaces Avramovic, who stepped down last year after leading Singapore to three championships in the Suzuki Cup, a biennial event organised by the ASEAN Football Federation.
Singapore is ranked 165 in the world by FIFA.