Agent Mike Conley Sr. of BDA Sports told ESPN.com that Cook has agreed to join the Bulls after going unclaimed through the NBA's waiver process this week.
Despite a number of teams that could use an extra shooter -- such as Minnesota and the Los Angeles Lakers -- Cook went unclaimed after being waived by Houston because any interested team would have had to have sufficient salary-cap space or a big-enough cap exception to absorb Cook's $3.1 million salary.
Cook won the NBA 3-point shootout in 2009 while playing for the Miami Heat. He cleared waivers at 5 p.m. ET Friday after being released Wednesday by the Rockets to make room for Houston's signing of James Anderson.
The Rockets, according to sources close to the situation, tried to find a new home for Cook via trade before letting him go but couldn't manufacture a taker willing to absorb the final year of Cook's deal.
Bulls coach Tom Thibodeau was asked about the possibility of Cook's arrival before Friday's game and did not want to show his hand regarding the potential move.
"When it happens, I'll have thoughts," Thibodeau said.
Information from ESPNChicago.com's Nick Friedell was used in this report.