Elwood represented Connacht 168 times as a player and won 35 caps for his country, appearing in two Rugby World Cups.
The 43-year-old has decided not to seek a renewal of his Connacht coaching contract which expires at the end of the season.
Confirming his decision to step down at the end of the 2012/13 campaign, Elwood said: "I have come to this decision after thinking long and hard about what is best for me and also what is best for Connacht.
"I have given a big part of my life to Connacht Rugby and I feel that it is time for me to have a change and time for the province to have a change as well.
"I want to stress that this has nothing to do with any on-field issues or performances or anything off the field.
"Connacht has progressed enormously in the last couple of years and I can only see that continuing, but for me personally the time is right to step aside at the end of this season and let someone else take things on."
He added: "It is a decision that I have not made lightly and it's an emotional one but again I would like to make it very clear that it is my decision and no one else's.
"I have not been under any pressure to step down and I have always received great support from the IRFU, the Professional Game Board and everyone involved with Connacht."
Connacht Rugby Chief Executive Tom Sears commented: "Eric Elwood is synonymous with Connacht Rugby and he will leave a big void. His decision has come as a surprise but it is one we respect and understand.
"Eric will remain in charge for the rest of the season and we will begin a recruitment process to find someone who can build on the foundations he has put in place and take us to the next level.
"We will look to appoint the very best person we can and they will be charged with delivering the results that will see Connacht challenge successfully on all fronts. The search will be comprehensive and global."