[Editor's note: The Houston Texans have officially announced signing Grossman as of 3:02 p.m. CDT Friday.]
The Houston Chronicle reported the story Thursday, and Grossman's agent, Drew Rosenhaus, confirmed the deal Friday on his Twitter page.
"Rex Grossman has officially signed with the Texans. He is excited about the opportunity to have a fresh start with the Texans," the agent's tweet read.
The contract, contingent on Grossman passing his physical, would be for $620,000, the minimum a seven-year veteran can receive.
Grossman, 29, was an unrestricted free agent but hasn't made any known visits prior to this.
A former first-round pick, Grossman spent six seasons with the Bears. He signed a one-year contract last year with the Bears but lost his starting job to Kyle Orton.
The Texans currently have Matt Schaub at quarterback, but are in need of a backup after trading Sage Rosenfels to the Minnesota Vikings. The Texans have already signed former Detroit Lions backup Dan Orlovsky.
ESPN.com senior NFL writer John Clayton contributed to this report.