Ellborg moves to Sunderland for £3m.
The 22-year-old has penned a contract with the Black Cats to 2030.
Ellborg said: “It feels amazing to have signed for this Club. The past few days have been enjoyable, from learning about the interest, getting to know the Club and the people, and finalising the move.
"The Club has had an excellent season so far, and I’m incredibly happy to be part of this journey. I’m aware of Sunderland’s history, and it means a lot to be part of something with such a rich tradition. I’m really looking forward to meeting everyone at the Stadium of Light on Monday and hopefully playing in front of the fans soon.”
Sunderland chief Kristjaan Speakman added: “Melker has enjoyed a very positive season in Sweden, breaking into the starting XI and producing standout performances in the Allsvenskan and the Europa League. Physically strong, he has the athleticism of a modern goalkeeper and is calm and composed in possession.
"Melker has a lot of potential, and we believe he is ready to take this step and join our squad. We are very much looking forward to working with him.”