Seventh-placed Posh fought off several fellow League One clubs to secure the midfielder’s services on loan for the rest of the season.
The 23-year-old was not included in Town boss Joey Barton’s squad for Saturday’s FA Cup defeat by AFC Wimbledon.
Dempsey, 23, had been a regular starter at Highbury in the previous two seasons, and was named young player of the year for 2016-17 while on loan from Huddersfield.
He made the move permanent that summer, penning a three-year deal.
He remained a first-team regular under both Uwe Rosler and John Sheridan but has found starts limited since Barton took the reins last summer.
Dempsey is now looking to help Peterborough to promotion and said: “It is a good opportunity for me to come to a club that is challenging at the top of the division, a division that I know well.
“I heard about the interest through my agent and as soon as Peterborough were mentioned it was a move I wanted to happen.
“I don’t know any of the lads but that can sometimes happen when you move to a new club, I am looking forward to getting to know them this week.
“I would describe myself as a box-to-box midfielder. I like to get forward and create and score goals, and that is what I hope I can bring to the club.
“I am an energetic player. I like to get up and down, and I hope I can help the club with a promotion push because the club are in a good position.
“It is down to me this week to impress the management and show what I can do.
“Hopefully I can get into the team for Saturday’s game with Rochdale.
“I can then try and impress the home supporters and show them what I am all about.”