Ellborg made a breakthrough during the 2025 season, at times relegating high-profile national-team signing Robin Olsen to the bench.
But he played only seven Allsvenskan matches for the Sky Blues. Sunderland, in the Premier League, are now buying the goalkeeper.
"The fact that Melker has been sold directly to a Premier League club is a testament to his work but also how we as an association work with our talents," says Malmö FF's sporting director Daniel Andersson in a statement.
The transfer fee is 42 million kronor, according to Expressen. It is a record for a goalkeeper from the Allsvenskan.
Sunderland are eleventh in the Premier League.
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