"Andrew is a fantastic professional and has risen to every challenge set before him," Arnold said.
"He has performed exceptionally well this season and is one of the reasons we're on track for our first goal of 50 points this season, and the remaining targets beyond that."
Redmayne is the second Sydney FC player to re-sign last week, after defender Michael Zullo, who put pen to paper on a two-year extension.
"It's so pleasing to be a part of a successful side and I'm glad to be remaining a Sky Blue," Redmayne said.
"At Sydney FC I feel I'm playing some of my best football and I'm glad to be continuing to train under [goalkeeper coach] John Crawley who has developed me into the player I am.