Simpson played a total of nine senior matches for Rangers, with his final appearance coming in last game of the 2021/22 campaign, a dead rubber away at Hearts.
Rangers say that they have received an undisclosed fee for Simpson, who has penned a deal with the Bluebirds until the summer of 2024.
A statement from Rangers on social media read: “Rangers can today confirm the departure of Jack Simpson to English Championship side Cardiff City on a permanent deal for an undisclosed fee.
“Simpson leaves Rangers with the best wishes of everyone at the club.”
On signing for Cardiff City, Simpson said: “I'm very excited to join the club. I spoke to the manager about what he's trying to do here.
"I'm a ball playing centre half, and hopefully that'll suit the way the team are playing now.
"I'm excited to be here. I want to help the team and play in as many games as possible."
City boss Steve Morison added: "Jack's going to bring balance for us in defence.
“He is a fantastic player, with a beautiful left foot. He is someone who wanted to come and be part of it. Jack's here with a smile on his face, and ready to get to work.
“He's an excellent addition to the group.”
Simpson was not signed in time to play in Cardiff’s EFL Cup tie on Tuesday evening against Portsmouth but could make his debut against Birmingham City in the Championship on Saturday.