Having joined Wasps from fellow Guinness Premiership side London Irish in 2007, Flutey was voted the Professional Rugby Players' Association Player of the Year in his first season with the English champions.
He will now join up with fellow England international Andy Goode and 2003 World Cup winners Steve Thompson and Ben Cohen at the 1997 Heineken Cup winners.
Capped at all age-group levels in his home country of New Zealand, Flutey qualified for England on residential grounds last year and has since been a regular starter in both the autumn series and the Six Nations.
Flutey was in fine form for England during last Saturday's defeat to Wales in Cardiff and has been talked about as a strong contender for a place in the Lions squad to face South Africa this summer.
A Lions spot would cap a remarkable turnaround for the New Zealand-born playmaker as he played against the Lions as a 67th-minute replacement for Wellington four years ago.