He will take over from Michael Bradley at the end of the season and will confirm his backroom team in the coming weeks.
Connacht CEO Gerry Kelly paid tribute to the contribution made to Connacht Rugby over the past six-and-a-half years by Bradley.
Elwood said he was really looking forward to the challenge and urged Connacht people to get behind the side as they continued to build the squad.
Elwood, who made 168 appearances for Connacht, has been assistant coach for the past four-and-a-half years.
Connacht will resume their Magners League campaign this Friday when they take on Glasgow Warriors at the Sportsground (kick-off 8pm).