The 47-year-old, who has joined the Reds from Austrian Bundesliga outfit TSV Hartberg, flew into the UK and met with Oakwell officials on Monday and has agreed to take over from Valerien Ismael whose departure to West Brom was confirmed last Thursday.
Barnsley will pay a release clause valued at around £300,000 to Hartberg.
Schopp said: “It’s great to come to a country where football is so big, so traditional, especially in South Yorkshire. There are so many clubs and they are so famous and Barnsley, for me, is one of those teams.
"I will help Barnsley get to where they have been in the last year, I will do everything for that.
“I appreciate this opportunity a lot and I look forward to getting to work, meeting the team and coaching staff and seeing the supporters back in the stadium soon.”
A former Austrian international midfielder, Graz-born Schopp - who represented Sturm Graz, Hamburg, Brescia, Red Bull Salzburg and New York Red Bulls in his playing career - has managed Hartberg since 2018.
He has also previously managed Sturm Graz's second team and been an assistant at another Austrian side in St Polten.
There had been some concerns that Schopp's arrival could be jeopardized by post-Brexit work permit rules which came into force in the UK on January 1.
Managers need to have worked for two consecutive years in what is designated as a top league or in three of the last five, but the Austrian Bundesliga qualifies under the banding criteria.
Co-chairman Paul Conway, said: "We are very excited that Markus has signed with Barnsley and will continue the growth of our football club.
“He has had a remarkable career as a player and has been phenomenal growing Hartberg in the Austrian Bundesliga on a small budget. I am sure all in the town of Barnsley and our 11,000 seasonal members can't wait for the season to start."
Schopp's arrival means that it is the third successive occasion that the club has brought in someone who has managed in Austrian football.
Valerien Ismael's previous job before joining the club last October was at LASK Linz and his predecessor Gerhard Struber arrived from Wolfsberger AC.