Bibby signed a reported one-year contract worth the veteran's minimum $1.4 million, according to the New York Post, after splitting last season with three teams.
The 33-year-old Arizona product finished the campaign with the Miami Heat, who fell to the Dallas Mavericks in the NBA Finals. Bibby averaged 7.3 points and 2.5 assists in 26-plus minutes over 22 regular season games with the Heat.
"Mike is a veteran point guard who we know can be successful in our system," Knicks interim general manager Glen Grunwald said. "He's an effective player who has a long track record of leading his teams to postseason success."
Bibby, the second overall pick in the 1998 draft, owns career averages of 15.2 points and 5.7 assists over 962 games with the Grizzlies, Kings, Hawks, Wizards and Heat.
Jeffries, 30, was waived by the Rockets last season and was picked up by the Knicks, with whom he had already spent three-plus seasons. The 6-foot-11 Indiana product has appeared in 552 career games with the Wizards, Rockets and Knicks.