The 51-year-old scored over 10,000 runs in an international career which consisted of 67 Tests and 221 one-dayers.
Flower joins Sussex after two years as batting coach for the Sri Lanka national side. He performed the same role for Pakistan between 2014 and 2019 and for Zimbabwe between 2010 and 2014.
"It gives me great pleasure to be added to the Sussex coaching staff and I can't wait to start," said Flower, younger brother of former England head coach Andy.
"I have been told about the exciting young batters coming through the ranks and am excited to be given the opportunity of hopefully improving them along their journey."
Grant's domestic coaching CV includes stints at Essex County Cricket Club and Midwest Rhinos in Zimbabwe.
His experience of the English game includes six seasons as a player with Essex from 2005 to 2010, during which time the team won three one-day trophies.