Bayern Munich had been linked with an almost customary annual swoop on Dortmund for Reus, whose previous deal included a €25 million release clause set to come into effect later this year.
However, that add-on is thought to have been scrapped in Reus' new contract, which runs to 2019.
While Reus' future at the club has been in doubt for much of Dortmund's disastrous Bundesliga campaign, Klopp insists he never had any doubt the Germany attacker would stay.
Furthermore the coach hopes Reus gets a hero's welcome when Dortmund host Mainz on Friday.
"It shows that Marco believes that we will fix it," said Klopp. "Marco believes in a successful future with Dortmund, and I hope we see it tomorrow night as well.
"I am very glad that he made his decision this early. It's an important sign for all of us. I am very happy for him, there was never a reason to doubt him.
"He got applauded in the dressing room yesterday, now it's more important he gets that again in the stadium on Friday."
Dortmund are looking for back-to-back wins on Friday after climbing off the foot of the table with a 3-0 win over Freiburg on Saturday.
