"The deal with Royale Union St Gilloise will be our largest to date based on the overall nature of the agreement and the fact that Besfort is our own player," said club manager Stefan Andreasson to the Allsvenskan club's website.
Zeneli started playing football in Elfsborg when he was six years old and has not played for any other club.
"I have mixed feelings, but of course it's incredibly fun to take the step into Europe. It's something you've dreamed of since you were little," said Zeneli.
"It feels a bit like Elfsborg here, very familiar, and they care about people. I've really gotten that feeling, so now it feels good that it's over."
The 23-year-old has signed until 2030.
