Sampson signed a minor-league contract with the Rangers on Tuesday that includes an invitation to spring training.
The Rays released Sampson on Aug. 4.
The Cubs traded Sampson and Manuel Rodriguez to the Rays on Tuesday in exchange for Josh Roberson, Sahadev Sharma of The Athletic reports.
Sampson (knee) was activated from the 60-day injured list and outrighted to Triple-A Iowa on Monday, Tim Stebbins of MLB.com reports.
Sampson (knee) completed his third rehab start at Triple-A Iowa on Saturday, tossing three innings and striking out two while allowing three earned runs on three hits and one walk.
Sampson (knee) will move up to Triple-A Iowa on Tuesday to continue his rehab assignment, Ryan Herrera of AllCHGO.com reports.
The Cubs transferred Sampson (knee) from the 15-day injured list to the 60-day IL on Monday, Maddie Lee of the Chicago Sun-Times reports.
Sampson underwent a meniscal debridement procedure on his right knee Friday, Andy Martinez of Marquee Sports Network reports.
Sampson was recalled Thursday from Triple-A Iowa and placed on the 15-day injured list with a right meniscus injury, Maddie Lee of the Chicago Sun-Times reports.
Sampson was optioned to Triple-A Iowa on Saturday, Sahadev Sharma of The Athletic reports.