"Scheiner will likely handle contracts and salary cap management while the Browns hire a personnel executive to oversee football operations," according to Schefter.
Scheiner has been at his post with the Cowboys since 2004.
And here's Schefter with more of the low-down on Cleveland's allure in this news:
"Cleveland has become a desirable NFL destination with Scheiner, Jerry Jones' right hand man, joining the team that's now under the guidance of new owner Jimmy Haslam III and new CEO Joe Banner.
Scheiner is one of numerous people around the league who have expressed interest in moving to Cleveland. And by the time the Browns complete their organizational makeover, many expect it to have an entirely different look with an all-star cast of executives and coaches."
Former President Mike Holmgren left the organization in late November.