The 22-year-old had appeared just four times in the Championship for Blackburn this season.
Palmer has become accustomed to Championship football, spending the last two seasons at Huddersfield Town and Derby County.
He reached the play-offs during both of his previous loan spells in the Championship and Bristol City will be hoping that he continues that trend as they sit just five points off the top six and are currently on a nine-game unbeaten run.
“My preferred position is playing centrally behind the striker, in an attacking role and hopefully create and score goals to help the team go and reach the play-offs,” Palmer told the club’s official website.
“We’re nine unbeaten at the minute, five points off the play-offs so hopefully I can get as many games as possible to help the team with goals, assists, play well and add something.”
Palmer joins two of his Chelsea team-mates at Ashton Gate – Jay Dasilva and Tomas Kalas – as he becomes the third player from Stamford Bridge to go to Bristol City on loan this season.
The midfielder acknowledged the role his fellow Chelsea loanees played in influencing his decision to join Lee Johnson’s side.
“I spoke to Jay when making the decision. He told me it was a great club to be at and it’s the right club for me,” Palmer continued.
“My first impressions are all good. I’ve walked around the stadium, got a feel for the place, I’ve met the staff and I’m raring to go. Hopefully I can repay the trust that the head coach has shown in me.
“The first day is always difficult, getting to know everyone but hopefully I can get down to business quickly, train with the boys and get to know everyone and hopefully produce the goods on the pitch.”