Gilbert is expected to receive a two-year deal, the source said.
Texas coach Charlie Strong is looking to reboot the Longhorns offense heading into his third season in Austin. He stripped offensive coordinators Shawn Watson and Joe Wickline of their play-calling duties after one game last season. Receivers coach Jay Norvell called plays for the final 11 games of Texas' 5-7 season.
Gilbert served as a graduate assistant on Art Briles' staff at Houston in 2005 and worked for two Briles proteges, Philip Montgomery and Dino Babers, during his rise through the coaching ranks.
"We have to work harder now," Briles said Thursday night from The Home Depot College Football Awards ceremony. "It's like when someone gets into your bank account and steals your identity."
Gilbert served as co-offensive coordinator for Tulsa under Montgomery and also coached quarterbacks and receivers. The Golden Hurricane offense averaged 502.8 yards per game this season and ranked No. 5 in passing offense and No. 6 in total offense among Group of 5 programs.
Before his one-year stint at Tulsa, Gilbert spent one year as co-offensive coordinator at Bowling Green and two years at Eastern Illinois with Babers. Under Gilbert's tutelage, Eastern Illinois quarterback Jimmy Garoppolo won the Walter Payton Award, the FCS equivalent of the Heisman Trophy, in 2013 and was drafted by the New England Patriots.
Gilbert also has eight years of experience coaching Texas high school football, most recently at Temple High School in 2011.
Strong pursued TCU co-offensive coordinator Sonny Cumbie for the offensive coordinator job, but Cumbie announced Wednesday that he had elected to stay with the Horned Frogs. Cal offensive coordinator Tony Franklin was also reportedly a candidate.
ESPN's Max Olson and Joe Schad contributed to this report.