The former Manchester United man O’ Shea had hoped to stay with the Black Cats despite the club having experienced consecutive relegation from the Premier League and Championship last term.
However, it was decided by the club’s new owner Stuart Donald and manager Jack Ross that his contract would not be renewed.
The Black Cats squad is expected to undergo a overhaul as they prepare for life in League One next season.
The 37-year-old O’Shea is now set to sign a one-year deal with the Royals.
O’Shea spent the past several seasons with the Black Cats after he left United.
He played under eight different managers during his time with the Black Cats.
Despite now being well-past his prime, O’Shea is still able to compete at the highest level and his experience and leadership could be important for the Royals next season.
By signing for the Royals, he will also be reunited with his former Sunderland team-mate Vito Mannone.
He will also have the option of joining Paul Clement’s coaching staff when his one-year deal comes to an end.
O’ Shea recently retired from international football after Ireland’s 2-1 win over the USA on Saturday.