Rice will become Opposition Analyst/Head Scout for Ireland, having been with Palace since September 2020.
He helped guide the Under-23s to promotion via the play-off final in May 2021, and returns to Ireland with the thanks and best wishes of everyone at Crystal Palace.
Upon departing, he said: "I would like to thank everyone at the club for making me feel so welcome over the last 12 months, in particular Paddy McCarthy and Shaun Derry who have been unbelievable for me.
"Leaving the club was not an easy decision but the opportunity to work at senior international level for my country was something I could not turn down as it has been an ambition of mine for a long time.
"I have absolutely loved my time here at Palace and I want to wish everyone the very best for the season ahead.
"I will still be a regular visitor to Selhurst for first-team and U23 games and I can’t wait to see this next crop of talent coming through."