Gaby Stieger, 49, repeatedly loitered outside the Oscar winner's house in Southwark, south London, and sent him love letters over five years.
She was also ordered not to have any contact with, or come within 200 metres of Redmayne or his immediate family, reported BBC.
The interpreter pleaded guilty to stalking at Camberwell Green Magistrates' Court on Wednesday.
The mother-of-three from Colindale, north London, believed they had been married in a former life and her face would "contort with rage" when she spoke about his wife, Hannah Bagshawe.
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She added, "He told you he was distressed but you ignored him."
Redmayne described the distress it caused him and his family in a statement read to the court.
"I always try to be open and friendly as support (from fans) is what gives me a career. I deeply regret having met Gaby Stieger - she harassed myself and my family intermittently over five years, leaving us distressed, unsafe and deeply unsettled," he said.