Allen, a rookie guard out of UW-Milwaukee and a former standout at Thornton Fractional High School in Harvey, Ill., joins Jaric, Vance Cooksey, Andre Emmett and Kyrylo Fesenko as the latest additions to the Bulls roster before their first practice on Tuesday.
Allem, whose brother Tony plays for the Memphis Grizzlies, averaged 8.6 points and 5.1 rebounds for UW-Milwaukee and made the Horizon League All-Defensive team.
Jaric is a seven-year NBA veteran who has played for the Los Angeles Clippers, Minnesota Timberwolves and the Grizzlies. He hasn't played in the NBA since the 2008-09 season and spent last season with Montepaschi Siena of the Italian League.
Cooksey, a 6-foot guard, averaged 8.8 points a game with the Rio Grande Valley Vipers and the Texas Legends of the NBA D-League last season. The 6-foot-5 Emmett played six games with the New Jersey Nets last season, and averaged 23.1 points a game with the Reno Bighorns in the D-League.