He has been a regular with Shannon in the All-Ireland League. The 22-year-old back rower has been released from his Munster contract (Academy) to pursue a season's rugby with Exeter Chiefs, the newly-promoted English side.
He leaves with Munster's best wishes on a one-year deal that the province's management believe will help in the development of his professional rugby career.
Speaking about the move, Munster coach Tony McGahan said: "Eoghan is undoubtedly a player of immense potential as evidenced at All-Ireland League and British & Irish Cup level last season.
"However, we believe it to be in his best interests at this stage of his development to pursue this offer from Exeter Chiefs, where the prospect of regular rugby at Premiership level will prove hugely beneficial."
Exeter Chiefs coach Rob Baxter said: "Eoghan is a player who I have been following now for quite some time. I first started talking to his agent before Christmas when I was looking to add hungry players to our squad.
"He has played some big games for Shannon and probably feels unlucky not to have progressed further in the Munster set-up.
"Eoghan came over to join in with some of our pre-season testing and showed up well - not many forwards beat Tom Johnson over 40 metres and 100 metres.
"He showed up well in the conditioned games we played and although he is not a household name, I think he may be a name for the future."
Grace will link up with a number of Irish players including club captain and brother of 'the Bull', Tom Hayes. Also in Exeter are former Connacht and Ireland 'A' player David Gannon, Ruaidhri Murphy, formerly of Leinster and the Ireland U-20s, as well as Gareth Steenson, the former Ireland U-21 out-half from Ulster, making for a strong Irish contingent at Exeter.