In a surprising moment, Carlisle announced the news following the Pacers' 113-108 win against the Washington Wizards in Indianapolis.
He appeared in four games total for Indiana, with his 17 points against the Wizards on Wednesday night his most since the trade.
"We thanked him for what he's brought for the last six or seven days," Carlisle said. "He brought a high level of professionalism and he's done a really good job.
"I don't mind announcing it because it's going to happen and what the heck. There's nothing wrong with speaking the truth. It's the rare instance where you get to thank a guy in the presence of his teammates. And these guys have an awful lot of respect for who he is and what he's accomplished in the league."
The 30-year-old Thompson appeared in 30 games with the Kings before the deal, averaging four points and four rebounds in 15 minutes.
Bulls coach Billy Donovan did not comment on Thompson's addition following the team's 125-118 victory against the Kings on Wednesday night, saying he hadn't seen Carlisle's comments.
However, Chicago has been searching for help in the frontcourt behind Nikola Vucevic since the start of the season. It will need to clear a roster spot before adding Thompson.
"Known Tristan for years. Great dude," Bulls All-Star DeMar DeRozan said following Wednesday's game. "Championship experience. Good friend of mine. Got the utmost respect for him off the court. Obviously, we all know what he brings on the court. So, I think this will be a great addition for us. What he's able to bring, veteran leadership, understanding what it takes to win a championship."
Information from ESPN's Jamal Collier was used in this report.