The Tykes have scored twice in their first four matches this season and boss David Flitcroft hopes the 23-year-old striker is the answer to his side's goalscoring problems.
"I'm really pleased to be here and I'm looking forward to it," Pedersen told the club's official website.
"I have always wanted to play in England. I think the game here will suit me. I'm impressed with the people and the set-up at Barnsley.
"I like it when a manager looks at each person as an individual and in David Flitcroft I can see he is that type of person.
"It was good to meet him and I feel very happy with the decision to come here.
"First and foremost I'm a striker, I like to get in the box and attack the ball and I like to score goals.
"There are some very big clubs in the Championship and it's a good league to be in.
"Barnsley create a lot of chances, so hopefully I will be the last one on the ball to score a lot of goals."
Pedersen, who made his debut for hometown club Hamar at the age of 15, joined Vitesse from Norwegian side Stromsgodset and has had previous loan spells at Valerenga and Odense.