The 20-year-old Trinidad and Tobago international, who can play as a full-back or wing-back, becomes the Robins’ ninth summer signing.
Cardines developed in the Arsenal academy before joining Palace at Under-16 level. He made his Premier League debut against Arsenal last season, completing the full 90 minutes against the champions.
The youngster was also part of the Palace squad that defeated Rayo Vallecano 1-0 to win the UEFA Conference League.
“I am really excited to get started. I know the history behind such a big club and I cannot wait to get playing,” said Cardines
“I want to score as many as possible, set up as many as possible and most importantly win as many games as possible.
“I have heard great things about the fanbase. I hope I can impress and am looking forward to meeting the supporters.”