The castle, west of London, is one of Queen Elizabeth's main residences. Its 15th-century chapel is as historic but more intimate than Westminster Abbey, where Harry's older brother, William, married Kate Middleton in 2011.
Harry's communications secretary, Jason Knauf, said Windsor "is a very special place for Prince Harry," and he and Ms Markle have regularly spent time there since they began dating about a year and a half ago.
He said the wedding "will be a moment of fun and joy that will reflect the characters of the bride and groom".
The royal family will foot the bill.
Kensington Palace said Ms Markle plans to apply for British citizenship, and will be baptised in the Church of England before she marries the fifth in line to the throne.
The couple will carry out their first official engagement on Friday, visiting a youth charity and a World Aids Day event in Nottingham.
For Ms Markle, who has left the TV series 'Suits' after seven seasons, it will be a first taste of life as a working royal.
Ms Markle's future sister-in-law Kate said she was "absolutely thrilled".