His move comes as part of a management shake-up aimed at bolstering its presence in the region.
Sources close to Mr Frazer said his move was a "reward for doing a good job in the UK". However, other Microsoft insiders said he had been dealt a bad hand in the reshuffle.
The South African-born executive will do a direct job swap with Michael van der Bel and report to Ralph Haupter, formerly head of Microsoft Germany, who has effectively overtaken him to take the top job in China.
Mr Haupter is replacing Simon Leung who has quit as chief executive for "personal and family reasons".
During his six-year stint in the UK, Mr Frazer was influential in calling for closer cooperation between business and higher education.
However, his tenure was blighted by a high profile court case which lifted the lid on alleged sexual harassment and a culture of boozing.
The case, which was brought by former Microsoft executive, Simon Negus, accused Mr Frazer of jumping the gun and trying to oust Mr Negus over alleged sexual harassment before a formal investigation into his behaviour had ended.
The case was settled and all charges dropped. However, it exposed an apparent culture of "excessive drunkenness" and lewd behaviour at Microsoft, causing severe embarrassment in the upper echelons of the business and denting morale at its UK arm.
In an internal email seen by The Sunday Telegraph, Mr Frazer acknowledged there had been "a few lows" during his tenure, but said he still regarded the UK division as Microsoft's "crown jewel" outside America.
"While there have been many highs as well as a few lows, our journey over this time in which we can all *Take Pride* [sic]," he wrote.
