The former Ireland outside-half will replace current director of rugby Michael Bradley who is stepping down after nearly seven years with the province.
Bradley's departure was announced back in November and Connacht have been have taken their time to assess their options ahead of the 2010/11 season.
Elwood, who made 168 appearances for Connacht scoring 318 points, has been assistant coach for the past four and a half years.
Connacht CEO Gerry Kelly stressed that Elwood's experience and knowledge of the province ultimately made his appointment a straightforward one.
"When we set up a sub committee to look at the coaching position for next season, we liked Eric's vision for the team and for Connacht Rugby," said Kelly.
"The decision became an easy decision for us. We have always stated that we want to promote Connacht coaches.
"Given Eric's record as a player and a coach, and his assistance to Michael over the last number of years, (appointing a coach) became an easy task.
"I first met Eric when he was 16 years of age. Since then he has played at all levels for Connacht. Except for a brief dalliance in Dublin with Lansdowne, all his rugby playing career and coaching career has been spent either with Galwegians or Connacht.
"The stats are there - 168 appearances for Connacht and 38 for Ireland - and I think that says an awful lot about the man."
Elwood began his coaching career with the junior section at Connacht and the 41-year-old has also coached his country at Under 20 level.
He has worked closely with both junior and senior players at the province and is hugely respected by everyone involved with Connacht Rugby.
"Towards the end of his playing career, Eric got involved in coaching the Under 20s at Connacht," added Kelly.
"He did a great job with them and that was a great help in recognising the young players that were coming through the system.
"He's been accredited at all coaching levels, including the highest level in Ireland - Level Three. Eric also coached the Ireland Under 20s to a Grand Slam."
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