The Bulls also waived guard Cameron Payne, who was in his third season in Chicago.
Memphis believed it had a deal including Brooks and Selden for Kelly Oubre Jr. in early December, but that deal fall apart when the Phoenix Suns were under the impression they were receiving Memphis' Dillon Brooks as part of a three-way deal.
Memphis has struggled lately and coveted the athletic playmaking ability of Holiday, who is averaging 11.6 points, 4.4 rebounds and 2.2 assists in 35 minutes per game.
Holiday is on an expiring contract and could be moved again before the Feb. 7 trade deadline as long as his contract is not aggregated with another player. However, by giving up the two second-round picks, it would seem Memphis' intent is to re-sign Holiday in the summer.
The Grizzlies remain $463,000 under the luxury tax with the $4.4 million addition of Holiday.
Payne, 24, has struggled to stay healthy and find traction in the league since the Oklahoma City Thunder selected him 14th overall in the 2015 NBA draft. He averaged 6.7 points, 2.1 rebounds and 3.1 assists in 18.8 minutes per game over three seasons with the Bulls.
ESPN front office Insider Bobby Marks contributed to this report.