South Africa all-rounder Philander suffered a groin injury in the Championship defeat by Kent.
Taylor, 32, has taken 126 wickets in 85 one-day internationals for the West Indies at an average of 28.16.
"We're delighted that we have agreed terms with Jerome," director of cricket Keith Greenfield said.
"Jerome is a vastly experienced international white-ball bowler and we believe he will be a great asset to [head coach] Mark Davis and our squad during the tournament."
Sussex have signed West Indies pace bowler Jerome Taylor for the One-Day Cup group stages as a replacement for the injured Vernon Philander.