Meredith confirmed the news during an appearance on ESPN 1000's Waddle and Silvy Show.
Bears general manager Ryan Pace and coach Matt Nagy met with Meredith to inform him of the decision.
"It was just the right move for the Bears as a whole and as a team. As for me, as a player, we just felt this was the best way to go," Meredith said.
"I think in the grand scheme of things, I don't really know the specific details why they did it, or why they didn't. I can just control what I can control and do going forward."
A source told ESPN's Adam Schefter that the Bears' call was mainly a medical decision as Meredith is coming off a torn ACL and MCL, and the team was hesitant to commit that much money to a player coming off such a serious knee injury.
Meredith said his injury rehabilitation has "been a big part of my offseason, making sure my knee and my recovery is right so I'm able to come back 100 percent."
He added: "With that being said, I haven't had any setbacks or anything like that. So I don't think anyone had that as a major concern."
Meredith gives the Saints another big target to pair with 6-foot-3, 212-pound Pro Bowl wideout Michael Thomas and veteran speedster Ted Ginn Jr. Meredith will likely compete with Ginn and Willie Snead for prominent roles in New Orleans' receiving corps.
The Bears had issued an original-round tender to Meredith, valued at $1.9 million, so the Bears receive no draft pick compensation from the Saints because Meredith was an undrafted free agent.
After going undrafted in 2015, Meredith signed with the Bears as a free agent out of Illinois State and appeared in 11 games as a rookie, catching 11 passes for 120 yards.
"An opportunity like this isn't presented to a lot of people. For me to be able to go down there and play with a first-ballot Hall of Famer and soak up all the knowledge he has about the game and see the game from a different perspective is exciting."
Cameron Meredith, on being able to play with Drew Brees
Meredith, 25, had a breakout season in 2016 with 66 receptions for 888 yards and four touchdowns, but suffered the knee injury in a preseason game last summer at Tennessee. He expressed confidence in January that he'll be ready by the beginning of training camp.
Joining the Saints reunites Meredith with wide receivers coach Curtis Johnson, who previously served in the same role for the Bears.
The Bears were aggressive in addressing the wide receiver position in free agency this winter, spending heavily to land Allen Robinson (three years for $42 million; $25.2 million guaranteed) and Taylor Gabriel (four years, $26 million; $14 million guaranteed).
The Saints had the No. 2 offense -- and the No. 5 passing offense -- in the NFL last season. But they had uncharacteristic struggles on third downs, finishing 19th in the league with a conversion rate of 37.6 percent, in large part due to Snead's struggles after he was so good in that role in years past.
Saints coach Sean Payton labeled the receiver position as a "must" during last month's league meetings after the team missed out on some other targets in free agency. The Saints made a strong push to re-sign tight end Jimmy Graham before they decided that his price tag was too high. They had scheduled a visit with receiver Jordy Nelson before he signed with the Oakland Raiders. They also re-signed veteran tight end Benjamin Watson two weeks ago.
During his breakout season in Chicago, Meredith spent at least half of his time in the slot -- which is where he could fit best in New Orleans, as well. But he has the versatility to play inside and outside.
Meredith said Wednesday that he is "extremely excited" to be able to play with Saints quarterback Drew Brees.
"An opportunity like this isn't presented to a lot of people. For me to be able to go down there and play with a first-ballot Hall of Famer and soak up all the knowledge he has about the game and see the game from a different perspective is exciting," Meredith said.
ESPN's Jeff Dickerson and Mike Triplett contributed to this report.