The 22-year-old right winger will be with the Scottish club until January.
Stobbs first played for Sheffield United in 2014, but has only managed five first team appearances since then.
He will be hoping to gain regular first team football at Livingston.
Stobbs was last on loan at Port Vale, where he played eight games in League One in 2017.
The winger is also capable of playing as a central striker.