Ginn ranks 25th in NFL history with 15,685 all-purpose yards -- including 5,702 receiving yards, nearly 10,000 kickoff and punt return yards and 42 total touchdowns.
His agreement with the Bears was first reported by NFL Network. GIbson's deal was first reported by the Houston Chronicle.
Ginn, 35, became expendable with the New Orleans Saints after they signed Emmanuel Sanders in free agency. But after 13 NFL seasons, Ginn said earlier this month that he had no intention of retiring, adding, "I've still got a few years left in me."
Chicago had a clear need at receiver after releasing veteran Taylor Gabriel this offseason. He was fourth on the club in receptions last year, but he missed a large portion of the season because of multiple concussions. In 2018, Gabriel caught a career-high 67 passes for 688 yards.
Bears receivers Allen Robinson, Anthony Miller and Cordarrelle Patterson are locks to make the 53-man roster, but the bottom of the depth chart is wide-open for 2020. Ginn will compete for the fourth or fifth receiver spots against Javon Wims, 2019 fourth-round pick Riley Ridley, 2020 fifth-round pick Darnell Mooney and veteran Trevor Davis, who signed on Wednesday.
Although his career got off to a slow start with the Miami Dolphins as the No. 9 overall pick in the 2007 draft, the 5-foot-11, 180-pound Ginn has maintained his reputation as one of the NFL's fastest players throughout his career with the Dolphins, San Francisco 49ers, Carolina Panthers, Arizona Cardinals and Saints.
Before he played football at Ohio State, Ginn was a national champion in the 110-meter hurdles in high school, and he was part of a 4x100-meter relay team his senior year that beat a team anchored by future Olympic champion Usain Bolt.
Ginn's production has dropped off over the past two years, thanks in part to a 2018 knee injury that sidelined him for 11 games. Although he played all 16 games for the Saints in 2019, he caught just 30 passes for 421 yards and two touchdowns.
Before the injury, however, Ginn had the best three-year stretch of his career -- after the age of 30 -- with the Panthers in 2015 and 2016 and the Saints in 2017. He averaged 50 catches, 759 yards and six touchdowns over those three seasons while serving primarily as a deep threat.
Gipson, 29, is expected to start alongside Pro Bowl safety Eddie Jackson in the Bears' revamped secondary.
Chicago allowed veteran Ha Ha Clinton-Dix to leave in free agency, but the Bears opted not to draft a safety with either of their two second-round picks. The Bears previously addressed the position earlier in free agency by signing Deon Bush and Jordan Lucas to one-year deals, but Gipson's projected 2020 salary makes him the clear favorite to start.
Gipson is still owed $3.25 million in guaranteed money from the Texans, who released him on April 28. Bush is guaranteed $637,500 next season; Lucas' guarantee is $340,000.
The Bears will additionally have a new starting cornerback next season opposite Kyle Fuller. Chicago drafted Utah cornerback Jaylon Johnson with the 50th overall pick after the team released Prince Amukamara in February.
Gipson played one season in Houston after he was released by the Jacksonville Jaguars. He started 14 games in 2019, finishing with three interceptions and 51 tackles.
He was placed on injured reserve before the Texans' wild-card playoff game against the Buffalo Bills because he aggravated a transverse process fracture in his lower back and suffered a broken wrist in Week 17. He originally suffered the back injury during the season, causing him to miss two games.
Gipson, who turns 30 on Aug. 7, has appeared in 112 games with 104 starts in his eight NFL seasons, spending time with the Cleveland Browns, Jaguars and Texans. He was a Pro Bowl selection in 2014 for the Browns when he had a career-best six interceptions.
ESPN's Adam Schefter, Jeff Dickerson and Mike Triplett contributed to this report.