Scottish football: Motherwell announce new manger
Kenny Black, McCall's assistant, will take the team for Saturday's home game with Ross County.
Black's future is unclear, with talks planned over the coming days to establish whether he will stay on.
Baraclough was one of six candidates interviewed for the post, with Terry Butcher taking himself out of contention this week.
Former players Mitchell van der Gaag and Rob Maaskant were spoken to, along with ex-Kilmarnock manager Kenny Shiels and Black.
"Short-term my aim is to keep this club in the Premiership," said Baraclough. "There is no easy way to go about that and it is a situation that hasn't been at this football club in a few years but it doesn't scare me.
"I feel as though there is more than enough to push us up the table in the short term then try and build for long term by producing players. I am big on development, so the young players will certainly have a pathway to the first team if they are good enough.
"I want to win trophies. Why not Motherwell Football Club? Why can't we win the Premiership?
"You've got to go out with that thinking otherwise you won't achieve anything. To have days out in the cup are great for fans, but they are important. It's a way into Europe and I've been used to that and want more of it, as I'm sure the fans do too."