Narine withdrew from the World Cup earlier this week, saying he required more time to be able to bowl confidently with his new action. The 32-year-old Miller has represented the West Indies in 45 One-Day Internationals and has taken 40 wickets with his left-arm spin.
His last ODI was against England in March 2014. The Event Technical Committee of the ICC Cricket World Cup approved the replacement.
"The replacement was approved as an exceptional circumstance," an ICC release said.
The Event Technical Committee of the ICC Cricket World Cup consists of Geoff Allardice (ICC General Manager Cricket, Chairman), Campbell Jamieson (ICC General Manager Commercial), John Harnden (Chief Executive, CWC 2015 LOC), Gavin Larsen (Cricket Operations Manager, New Zealand), Russel Arnold and Sanjay Manjrekar (independent nominees).
The West Indies in in Pool B with defending champion India, Ireland, former winner Pakistan, African rivals South Africa and Zimbabwe, and qualifier United Arab Emirates (UAE). The West Indies will play its opening match against Ireland at Saxton Oval in Nelson on February 16.