Connacht confirmed the move, which will see Elwood replacing current incumbent John McKee, today - just three days after the westerners' long-standing number 10 ended his playing days with defeat to Sale.
The 36-year-old Elwood came on as a second-half replacement but could do little as the Sharks powered to a 59-9 Challenge Cup semi-final second leg win.
Connacht CEO Gerry Kelly said: "Eric has given tremendous service to Connacht over the past 17 years and we are delighted that he is now going to take up a coaching role with the province.
The province's Director of Coaching Bradley recently signed a new two-year deal. Elwood - who is due to complete his Level Three coaching course next month - will take charge of the Connacht backs from July onwards.
The duo played together for Ireland on eleven occasions including 1993's famous 17-3 Five Nations defeat of England at Lansdowne Road.