In August, a Cabinet Office Report recommended that Paul Scott be replaced as chair of the group.
It found relations behind the scenes were "broken", and it would be at least another year before another planning application could be submitted.
Mr McSorley is a former council boss.
He served as chief executive of Omagh District Council and was later interim chief executive of Strabane District Council from 2011 to 2015.
Sports Minister CarÃ¡l NÃ­ ChuilÃ­n has welcomed Mr McSorley's appointment and wished him "every success in helping to bring the Casement Park project to fruition".
She said Mr Scott had "played an important role in providing technical advice and guidance in relation to the stadia programme and, as Casement Park progresses, he will continue to play an important role".
"Although the skill-set of the chair of the group has been redefined, Paul's safety and technical expertise will remain vital to the STG and to the overall project," she added.
The Cabinet Office report was commissioned after Mr Scott told a Stormont committee in April that the emergency-exiting arrangements in the proposed 38,000-capacity stadium were flawed.
Danny McSorley has been appointed as chair of the safety technical group (STG) overseeing the planned new stadium at Casement Park in west Belfast.