The 23-year-old joins Palace on an 18-month deal, running until the summer of 2027.
The former Athlone Town striker bagged 26 goals for the League of Ireland side in all competitions last year, firing them to a league title and an FAI Women's Cup.
Capping off her brilliant season, Brady swept the major individual honours, winning both the SSE Airtricity Women’s Premier Division Golden Boot Award and the Player of the Year Award.
Her fine league form earned her a call-up to Carla Ward's Ireland squad last November, where she joined Palace teammates Abbie Larkin, Hayley Nolan, and Ruesha Littlejohn in the matchday squad for the fixture against Hungary.
Brady will be eligible to face Sheffield United on Monday evening.
Manager Jo Potter said: "Kelly is an exciting young talent, and we are very happy to have her here at Palace.
"She's coming off a great season, and her goalscoring ability is going to be a huge asset for us."
Speaking on her move to Palace, Brady said: "It feels surreal to be here, I can't wait to be involved in the great things the girls have been doing this season."